2 feet Opposite sides of a rectangle are equal. All sides of a square are equal. 2 X 3 = 6 meters = 18 meters
|
|
- Irma Montgomery
- 7 years ago
- Views:
Transcription
1 GEOMETRY Vocabulary 1. Adjacent: Next to each other. Side by side. 2. Angle: A figure formed by two straight line sides that have a common end point. A. Acute angle: Angle that is less than 90 degree. B. Complimentary angles: Two angles that add up to 90 degrees C. Degree: Measure of the size of an angle. D. Obtuse angle: Angle that is greater than 90 degrees and less than 180 degrees. E. Rays: The sides of an angle. F. Reflex angle: An angle that is more than 180 degrees and less than 360 degrees. G. Right angle: Angle that is 90 degrees. H. Straight angle: An angle that is 180 degrees. I. Supplementary angles: Two angles that add up to 180 degrees J. Vertex: The point at which two rays of an angle come together. K. Vertical angles: When two line intersect it is the pairs of nonadjacent angles. 3. Circle: A shape in which all points are an equal distance from a point, the center. A. Circumference: Distance around the outside edge of a circle. B. Diameter: Straight line distance from one side of a circle to the other side, going through the center. C. Radius: Distance from the center to the outside edge of a circle. 4. Congruent: Exactly the same size and shape. 5. Parallel: Two lines that are always the same distance apart. They never intersect, no matter how far they are extended. 6. Parallelogram: Quadrilateral in which the opposite sides are parallel and equal. 7. Perimeter: Distance around the outside edge of a figure. 8. Perpendicular: Two lines intersecting at a 90 degree angle. 9. Polygon: Closed figure made up of line segments. A. Regular polygon: Polygon in which all sides and angles are equal. B. Vertices: Corner point. 10. Polyhedron: Solid figure with flat faces. A. Faces: Flat sides of a figure. B. Edges: The shared surface where two faces meet. C. Prism: A polyhedron with parallel bases. D. Cylinder: A round polyhedron with flat ends, shaped like a can of vegetables. E. Vertice: Corner point. 11. Quadrilateral: A closed four sided figure.
2 12. Reflection: To flip a figure, as in a mirror image. 13. Rhombus: A figure that has four equal sides with opposite sides being parallel. 14. Rotation: Turning of a figure. 15. Semi: Prefix that means half. 16. Shift: Sliding of a figure to a new location. 17. Similar: The same shape, but a different size. 18. Square: A figure which has four equal sides, opposite sides parallel, and adjacent sides perpendicular. 19. Symmetry: A figure in which the two halves are mirror images of each other. 20. Trapezoid: A four sided figure that has one pair of parallel sides. 21. Triangle: Closed three sided figure. A. Scalene triangle: All sides have different lengths. B. Isosceles triangle: Two sides have equal length. C. Equilateral triangle: All three sides have an equal length. D. Right triangle: One of the angles is 90 degrees. Perimeter The perimeter is the distance around the outside edge of a figure. When the figure is a polygon it is the sum of the lengths of the sides. When the figure is curved it is the length of the curved line. The perimeter of a circle is also called the circumference. Square Rectangle 3 meters 6 meters 2 feet Opposite sides of a rectangle are equal. All sides of a square are equal. 2 X 3 = 6 meters = 18 meters Perimeter = 4 X 2 = 8 feet 2 X 6 = 12 meters The perimeter is 18 meters
3 Polygon 1 yd 2 yd. 5 yd. 3 yd 3.5 yd 4 yd = 18.5 yards The perimeter is 18.5 yards. The perimeter/circumference of a circle is found using one of the two following formulas: C = 2 R C = d C is circumference Is 3.14 or 22/7 R is the radius D is the diameter 5cm 14 in C = (2)(3.14)(5) = 31.4 The circumference is 31.4 cm. C = (22/7)(14) = 44 in. The circumference is 44 in.
4 Problems Find the perimeter of the following figures 1. Regular hexagon 8 inches 2. Equilateral triangle 11 centimeters 3. Square 6 meters 4. Rectangle 3 yards 9 yards
5 5. 9mm 7mm 5mm in 6 in 5in 7in 11in 7. 4m 3m 5m 8.Rhombus 10yd
6 8. Parallelogram 29 mm 18mm 9. Trapezoid 17ft 9ft 16ft 25ft
7 10. Find the circumference of each circle. A. E. 5cm = 3.14 = cm B. F. 14cm = 22/7 15cm = 3.14 C. G. 8m = m = 22/7 D. H. 70m = 22/7 21m = 22/7 Find the perimeter of each semicircular shape 11. A. = 22/7 B. 10m 28cm = Find the quarter circle perimeter. 5cm = 3.14
8 13. Find the circumference of the circle that is located inside the square. 10 cm 14. The curve is made up of two semicircles. Find its length. = m 8 m
9 15. Find the circumference of the following circles. = 3.14 A. Radius is 4 centimeter. D. Diameter is 18 inches. B. Radius is 12 meters. E. Diameter is 16 feet C. Radius is 5.5 miles. F. Diameter is 6.6 km 16. The length of the three sides of a triangle are 3.cm, 5.2cm, and 8.4 cm. Find the perimeter. 17. The length of three sides of a triangle are 7.5 in, 6.1in, and 4.9in. Find the perimeter. 18. The lengths of two sides of an isosceles triangle are each 2 1/2 cm. The third side is 3 cm. Find the perimeter. 19. The length of each side of an equilateral triangle is 4 1/2 in. Find the perimeter. 20. A rectangle has a length of 8.5 meters and a width of 3.5 meter. Find the perimeter. 21. Find the perimeter of a rectangle with length of 5 1/2 ft. and a width of 4 ft. 22. Find the perimeter of a regular pentagon that measures 3.5 in. on each side. 23. The length of each side of a square is 12.2cm. Find the perimeter. 24. Find the perimeter of a square that is 0.5m on each side. 25. What is the circumference of a circle with a diameter of 1.5 inches. Pi = The diameter of a circle is 4.2 ft. What is the circumference? Pi = The radius of a circle is 36cm. Find the circumference. Pi = Find the circumference of a circle that has a radius of 2.5 m. 29. How many feet of fencing should be purchased for a rectangular garden that is 18 ft long and 12 ft wide? 30. How many meters of binding are required to bind the edge of a rectangular quilt that measures 3.5m by 8.5 m. 31. The length of a rectangular park is 55yd. The width is 47yd. How many feet of fencing are needed to surround the park? 32. The perimeter of a rectangular playground is 440ft. If the width is 100ft, what is the length of the playground? 33. A rectangular vegetable garden has a perimeter of 64ft. The length of the garden is 20 ft. What is the width of the garden? 34. Each of two sides of a triangular banner measures 18in. If the perimeter of the banner is 46 in, what is the length of the third side of the banner? 35. The perimeter of an equilateral triangle is 13.2cm. What is the length of each side? 36. The perimeter of a square picture frame is 48in. What is the length of each side? 37. A square rug has a perimeter of 32ft. What is the length of each side? 38. Find the length of molding needed to put around a circular table that is 4.4ft in diameter. Pi = A bicycle has a tire diameter of 24 inches. How many feet does the bicycle travel when the wheel makes eight revolutions? Pi = Bias binding is sewed around the edge of a rectangular tablecloth measuring 72in by 45in. If the bias comes in packages containing 15ft of binding, how many packages of bias are needed for the tablecloth?
10 Area The formula for the area of a rectangular shaped figure is A=LW, where L is the length and W is the width. (In a square the length and width are the same.)(a square unit and a unit squared mean the same thing.) 2ft 4m 5ft A =5 X 2 = 10 square feet or 10 feet squared 4m A =4 X 4 = 16 square meters or 16 meters squared The formula for the area of a circular shaped figure is A= R 2, where R is the radius of the circle. Is represented by 3.14 or 22/7 3ft 7m A = 3.14 X 3 2 =28.26 square feet Or feet squared A = 22/7 X 7 2 = 154 square meters or 154 meters squared The formula for a triangular shaped figure is A = 1/2 bh, where b is the base of a triangle and h is the height of a triangle. 8in 7ft 15in A = (1/2)(15)(8) = 60 square inches or 60 inches squared 6ft. A = (1/2)(6)(7) = 21 square feet or 21 feet squared
11 The formula for the area of a parallelogram is A =bh, where b is the base and h is the height 5in A = 10 X 5 = 50 square inches 0r 50 inches squared 10in The formula for the area of a trapezoid is A = 1/2 (b 1 + b 2 )h where b 1 and b 2 are the two bases (the two parallel sides) and h is the height. 10cm A = (1/2 )( )(8) = 112 sq. cm. 8cm or 112 cm. sq. 18cm Area Problems 1. 6ft rectangle 2ft 2. 7in triangle 8in 3. 7yd 3yd rectangle
12 4. triangle 22cm 17cm 5. 12m 12m in rectangle 5in 7. 7cm square 8. 19ft 27ft rectangle
13 9. 2m triangle 21 m ft triangle 17ft 11. 9ft trapezoid 6ft 16ft 12. 6m 8m trapezoid 10m 13. 4yd 3yd trapezoid 9yd
14 Find the area of the circles below. = 3.14 Find the area of the circles below. = 22/ cm 7cm m 14m cm 14cm m 7om 22. We have a circle inside a square. What is the area of the circle? = cm
15 23.Find the area of the quarter circle. = cm 24.Find the area of each semicircle. = 22/7 A. B. 28m 7m 25. The following figures are made up of semicircles and quarter circles. Find the area of each figure. =22/7 A. B. 7cm 7cm 7cm 7cm 7cm C. 7cm 7cm 7cm
16 26.The following figures are made up of semicircles and quarter circles. Find the area of each figure. = 3.14 A. B. 10 in 10in 4in 4in C. 2cm 27. Find the area of the striped parts. A. Figure shows a square and a circle. = 22/7 B. Figure shows a square and 4 quarter circles 14 ft. = cm 10cm C. Figure shows a square and two semicircles = yd
17 28. The figure is made up of a rectangle and two semicircles. = What is its area? 10yd 12yd 29. The figure is made up of a triangle ad a semicircle. = 3.14 What is its area? 12cm 10cm 30. The figure shows a rectangle and a semicircle. = 22/7 7m 11m What is the area of the striped portion of the figure? 31. The figure shows a square and two semicircles. = in 2in What is the area of the striped portion of the figure?
18 32. The rectangle shows a rectangle and two semicircles. = cm 35cm What is the area of the striped portion of the figure? 33. The figure is made up of a square, a semicircle, and a triangle. = in 8 in What is the area and the perimeter of the figure? 34. The figure shows a square, a semicircle, and a quarter circle. = ft. What is the area and perimeter of the striped portion of the figure?
19 Volume The volume of a rectangular box is determined by the formula V = LWH. V represents volume. L represents length. W represents width. H represents height. 2ft 3ft 4ft V = 4 X 3 X 2 = 24 cubic feet /feet cubed The volume of a cylinder is determined by the formula V = R 2 h V represents volume Is represented by 3.14 or 22/7 R is the radius of the end. h is the height of the cylinder 4in V = (3.14)(4 2 )(6) V = cubic inches/inches cubed 6in
20 Problems Find the volume of the following figures cm 4m 5m 5cm 3m 3. 15yd 12yd 4. 9in 5in
21
22
23
24
25
26
27
28 Angles 1. Angle: A figure formed by two straight lines that have a common end point. A. Acute angle B. Circle: contains 360 degrees C. Complementary angles: Two angles that add up to 90 degrees D. Degree: The measure of the size of an angle. E. Obtuse angle: An angle that is greater than 90 degrees and less than 180 degrees. F. Rays: The sides of an angle G. Reflex angle: An angle that is more than 180 degrees and less than 360 degrees. H. Right angle: Angle that is 90 degrees I. Straight angle: An angle that is 180 degrees J. Supplementary angles: Two angles that add up to 180 degrees. K. Vertex: The point at which the two rays of an angle come together. L. Vertical angles: When two lines intersect it is the pairs of nonadjacent angles. acute angle right angle obtuse angle straight angle reflex angle Angles are typically named in one of two different ways x 1 C The angle is labeled by a single letter or number. A B The angle is named using three points with the vertex always being in the middle. This is called angle CAB or angle BAC
29 The size of an angle is usually designated by one or more curved lines. 70 o 315 o 130 o 70 o Be careful when a diagram has Multiple curved lines. Be aware where the angle starts and ends. The following are symbols that are commonly used. ABC This reads This is a symbol Symbol for two lines Parallel Triangle angle ABC for a right angle that are perpendicular, form right angles. Parts with the same number of slash marks are same size. Could be more than one slash mark. D C C A B D A B Complementary angles Supplementary angles BAC and CAD add up to 90 o BAC and CAD add up to 180 o
30 Assignments 1. How many degrees are in a right angle? 2. How many degrees are in a straight angle? 3. What is the complement of a 62 degree angle? 4. What is the complement of a 13 degree angle? 5. What is the supplement of a 48 degree angle? 6. What is the supplement of a 106 degree angle? 7. What is the complement of a 7 degree angle? 8. What is the complement of a 76 degree angle? 9. What is the supplement of an 89 degree angle? 10. What is the supplement of a 21 degree angle? 11. What is the complement of a 69 degree angle? 12. What is the complement of a 31 degree angle? 13. What is the supplement of a 162 degree angle? 14. What is the supplement of a 72 degree angle? G 15. C 16. A 48 o B 79 o o D E F angle AOB is straight angle angle DEF is straight angle How big is angle AOC? How big is angle FEG? 16. X W 17. P R 51 o 29 o Z Y O N How big is angle ZYW? How big is angle NOR?
31 18. C D 19. G F 30 o 40 o 80 o 38 o B A E D How big is angle ABC? How big is angle DEG? 20. Z 21. R V 94 o 22 o 59 o A Y X 195 o F How big is angle VYX? Going counterclockwise K from point A, how big is Angle AFK? C B 68 o A 210 o E D How big is the unlabeled angle CBA F How big is the unlabeled angle DEF? 24. What kind of angles are the following? A. B. C.
32 D. E. F. Solve for X X 140 o 3X 160 o X X 145 o X + 18 X 74 o X 42 o X 74 o 29 o A B C Angle ABC is a straight angle
33 X X 67 o 3X 2X 172 o A B C ABC is a straight angle X X 3X 4X 4X A B C 5X ABC is a straight angle 6X
34 Following are a number of properties that can help us determine the size of angles 1. Vertical angles are equal. Vertical angles are the nonadjacent angles formed by the intersection of two lines. C A B D A and B are vertical angles C and are vertical angles 2. Parallel lines that are intersected by a transversal form multiple pairs of equal angles. Parallel lines are always the same distance apart. AB and CD below are parallel. Transversals of parallel lines intersect both parallel lines. EF below is a transversal. A G B E C H D F A. Alternate interior angles formed by parallel lines and a transversal are equal. Alternate interior angles are on opposite sides of a transversal. AGH and DHG are alternate interior angles CHG and BGH are alternate interior angles B. Corresponding angles formed by parallel lines and a transversal are equal. Corresponding angles are in the same relative position in relation to separate parallel lines. DHG and BGE are corresponding angles. DHF and BGH are corresponding angles. CHF and AGH are corresponding angles. CHG and AGE are corresponding angles.
35 3. The sum of the interior angles of any n-gon is (n 2)(180 o ). N is the number of sides of the polygon. On the surface this may appear to be a confusing statement. Closer examination shows that it is actually quite simple. A. Let s look at the triangle shape. It has three sides. Therefore n = 3. (3 2)(180 o ) = 180 o. All triangles have 180 interior degrees. B. Let s look at the quadrilateral shape. A quadrilateral has four sides. Therefore n = 4. (4 2)(180 o ) = 360 o. All quadrilaterals have a total of 360 interior degrees. C. The same formula holds true regardless of the number of sides. 4. All the angles in an equilateral triangle are the same size. All the sides in an equilateral triangle are the same size. 5. The angles opposite the equal sides of an isosceles triangle are the same size. An isosceles triangle has two sides that are the same size. A B C Since AB = AC ABC = ACB 6. The opposite angles of a parallelogram are equal. A B D C AD BC and AB DC, therefore ABCD is a parallelogram. Therefore, ABC = ADC and BAD = BCD.
36 Assignments o 2. X X 45 o What is angle X? What is angle X? o L1 3X X A L2 B L1 and L2 are parallel lines. How big are angles A and B? o L1 6. L1 A 136 o B A B L2 L2 L1 and L2 are parallel lines. L1 and L2 are parallel lines. How big are angles A and B How big are angles A and B? X + 39 o 5X L1 L1 4X 2X L2 L1 and L2 are parallel lines. L2 L1 and L2 are parallel lines.
37 What is X? What is X? 9. One angle in a triangle is a right angle and one angle is 30 degrees. What is the third angle? 10. Two angles of a triangle are 42 degree and 103 degrees. What is the third angle? C 12. A Y 13. X B 134 o 116 o What is angle Y? This is an isosceles triangle. What is angle X? A B X 125 o D 38 o C X ABCD is a trapezoid What is angle X? AB and DC are parallel o What is angle X? S X X R P 112 o PQRS is a rhombus. Q This figure is a square.
38 What is angle X? What is angle X? 18. S 19. A B P 118 o X X R D C Q 25 o ABCD is a trapezoid. T AB and DC are parallel. PQRS is a parallelogram. What is angle X? What is angle X? 20. A B 21. A 50 o X 104 o X D B E C D ABCD is a parallelogram. C ABCD is a rhombus. Angle EDA is 60 o What is angle X? What is angle X? E 23. A B 24. X 46 o D A X D 35 o 112 o C C B ABCD is a parallelogram. ABCD is a parallelogram. Angle BAC is a right
39 What is angle X? angle. What is angle X? 25. A 26. A X D D 64 o 48 o X B B C E Angle DCB is 26 degrees. C What is angle X? Angle CBD is 18 degrees. What is angle X? 27. F 28. J M A E X P N 50 o 116 o X B C D ABDE is a trapezoid. K L What is angle X? JKLM is a square. 29. A D 30. Angle KPM is 116 o. What is angle X? C F F X B X C 38 o E D E G ABCD is a rectangle. FCD is an equilateral CDEF is a parallelogram.
40 triangle. What is angle X? What is angle X? 31. F E 32. F 120 o E A D D C X 110 o A B B C ABCD is a parallelogram. ABCD and ADEF are parallelograms Angle ADC is 110 o. AB = BF What is angle FAB? What is angle X? 33. D 34. A X E A 40 o D X 32 o B C B C 40 o ABCD is a parallelogram. E ABCD is a rhombus. What is angle X? What is angle X? 35. D C 36. E D X F X 40 0 C 28 o A B A B ABDE is a rectangle. ABCD is a parallelogram. BCDF is a rhombus. What is angle X? What is angle X?
Algebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
More information2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
More informationChapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationAngle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
More informationShape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
More informationIntermediate Math Circles October 10, 2012 Geometry I: Angles
Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,
More informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More information43 Perimeter and Area
43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study
More informationArea of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
More information2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?
MATH 206 - Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationof surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationCHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.
TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has
More informationCalculating Area, Perimeter and Volume
Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your
More informationArea of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
More informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More information9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationGeometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes
More informationGrade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationSA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid
Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical
More informationMENSURATION. Definition
MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters
More informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS - SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
More informationArea. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
More informationMEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.
MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units
More informationThree-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures
SHAPE NAMES Three-Dimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere Two-Dimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. [triangle] [cone]
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationGeometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
More information2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
More informationTallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
More informationApplications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
More informationPerimeter. 14ft. 5ft. 11ft.
Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine
More informationChapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
More information11.3 Curves, Polygons and Symmetry
11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationPerimeter is the length of the boundary of a two dimensional figure.
Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose
More informationAlgebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More information12 Surface Area and Volume
12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids
More informationGrade 8 Mathematics Geometry: Lesson 2
Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd
More informationGeometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment
Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points
More informationSolids. Objective A: Volume of a Solids
Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More information" Angles ABCand DEFare congruent
Collinear points a) determine a plane d) are vertices of a triangle b) are points of a circle c) are coplanar 2. Different angles that share a common vertex point cannot a) share a common angle side! b)
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationGeometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationSURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
More informationGEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
More informationExercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
11 MENSURATION Exercise 11.1 Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? (a) Side = 60 m (Given) Perimeter of
More informationShow that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.
Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional
More informationTeaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons
CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 4-6 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining
More informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
More informationLine Segments, Rays, and Lines
HOME LINK Line Segments, Rays, and Lines Family Note Help your child match each name below with the correct drawing of a line, ray, or line segment. Then observe as your child uses a straightedge to draw
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
More informationEstimating Angle Measures
1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle
More informationArea of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
More informationArea and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
More informationMATH STUDENT BOOK. 6th Grade Unit 8
MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF
More informationTEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM
7 th Grade Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in
More informationChapter 18 Symmetry. Symmetry of Shapes in a Plane 18.1. then unfold
Chapter 18 Symmetry Symmetry is of interest in many areas, for example, art, design in general, and even the study of molecules. This chapter begins with a look at two types of symmetry of two-dimensional
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More informationWhich two rectangles fit together, without overlapping, to make a square?
SHAPE level 4 questions 1. Here are six rectangles on a grid. A B C D E F Which two rectangles fit together, without overlapping, to make a square?... and... International School of Madrid 1 2. Emily has
More informationVOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.
Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:
More informationGEOMETRY (Common Core)
GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
More information12-1 Representations of Three-Dimensional Figures
Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular
More informationArea of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in
More informationChapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem!
Chapter 11 Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret
More informationCumulative Test. 161 Holt Geometry. Name Date Class
Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2
More informationDefinitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
More informationGeometry Notes VOLUME AND SURFACE AREA
Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate
More informationDiscovering Math: Exploring Geometry Teacher s Guide
Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional
More informationChapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
More informationThe GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
More informationUnit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
More informationGeometry EOC Practice Test #3
Class: Date: Geometry EOC Practice Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which regular polyhedron has 12 petagonal faces? a. dodecahedron
More information1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?
Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is
More informationSummer Math Packet. Post Geometry Honors
Summer Math Packet for Post Geometry Honors (for students who have completed Geometry Honors) Name Please read the directions (separate document) completely before starting your packet Print out the packet
More information1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
More informationAssessment For The California Mathematics Standards Grade 4
Introduction: Summary of Goals GRADE FOUR By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare
More informationCourse 2 Summer Packet For students entering 8th grade in the fall
Course 2 Summer Packet For students entering 8th grade in the fall The summer packet is comprised of important topics upcoming eighth graders should know upon entering math in the fall. Please use your
More informationCIRCUMFERENCE AND AREA OF A CIRCLE
CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given
More informationComprehensive Benchmark Assessment Series
Test ID #1910631 Comprehensive Benchmark Assessment Series Instructions: It is time to begin. The scores of this test will help teachers plan lessons. Carefully, read each item in the test booklet. Select
More informationFinal Review Geometry A Fall Semester
Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More information