Ch 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and Angles [and Triangles]


 Laureen Weaver
 1 years ago
 Views:
Transcription
1 h 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and ngles [and Triangles] Warm up: Directions: Draw the following as accurately as possible. Pay attention to any problems you may be having. You draw a figure using measuring tools, such as a protractor and a ruler. The lengths and angle measures need to be fairly precise. Mark the measures in the diagrams. Duplicate will mean to make an exact copy. Draw a duplicate line segment. Draw D. Draw a duplicate angle. Draw m = m. Do the length of the sides matter? Why? No, they are rays. Duplicate the triangle. Draw TRI by measuring only the side lengths. I MUST match up vertices! Draw an Equilateral Triangle. Draw equilateral triangle EQU, with sides all equal to. T R an t do with out an angle measure or a compass! U an t do with out an angle measure or a compass! Need to locate where the 2 sides meet! E Q Did you have any problems with making the drawings accurate? What were the issues? Yes, you can t figure out how the sides meet. You would have to just guess at it, because you don t have angle measures. S. Stirling Page 1 of 16
2 h 3 Worksheets S15 KEY LEVEL 2 Name EXERISES Lesson 3.1 elow is Page #1 3, 7, 8, 17 Use only a compass and a straight edge unless the instructions say to draw or measure! 1. Duplicate the line segments below them. 1) Use compass to measure. 2) With point on, use compass to make an arc, label intersection. Repeat for the other segments. D E F 1) Use compass to measure 2. onstruct line segment XY with length + D.. 2) With point on X, use compass to make an arc. 3) Use compass to measure D. 4) dd on the length, use compass to make an arc, label intersection Y. 3. onstruct line segment XY with length + 2 EF D. 1) Make a segment equal to + 2EF as you did before. 7. Duplicate triangle by copying the three sides, SSS method. 2) With point on the last arc, make a segment equal to D toward the left. Label intersection Y. Follow the Notes page 1. I 8. onstruct an equilateral triangle TRI. Each side should be the length of this segment. Follow the Notes page 1. T R 17. Use your ruler to draw a triangle with side lengths 8 cm, 10 cm, and 11 cm. Explain your method! Labels were provided to make the explanation clearer. 1) Draw a segment on the ray, = 11 cm. 2) Measure 10 cm with your compass. Swing an arc with center. 3) Measure 8 cm with your compass. Swing an arc with center. Label the intersection of the two arcs. 4) onstruct sides and. S. Stirling Page 2 of 16
3 h 3 Worksheets S15 KEY LEVEL 2 Name 3.2 onstructing Perpendicular isectors Investigation 1: () Using the definitions from your notes, draw the following. Remember that when you draw, you are measuring, so remember to write your measures in your diagrams! Write down your steps too. Draw at least 3 bisectors of. Draw a perpendicular bisector Draw D, the perpendicular bisector of. How many bisectors can you draw through one point? Infinite Is it possible to draw more than one perpendicular bisector? No () In the drawing is the perpendicular bisector of EG. Using your ruler measure the distance of point,, and D from the endpoints of EG. Label them. What do you notice? G The distance from any one point on the perpendicular bisector is the same distance from endpoints E and G. E Is this true for any segment bisector? Draw a counterexample. Must be a perpendicular bisector. is closer to G than E. D S. Stirling Page 3 of 16
4 h 3 Worksheets S15 KEY LEVEL 2 Name EXERISES Lesson 3.2 elow is Page #1 3 and Exercise #12. Use only a compass and a straight edge on this page! Use only a compass and a straight edge on 1 3! 1 & 3. onstruct the perpendicular bisector of then construct the perpendicular bisector of EF at the right. Since EF is too close to the edge, you Follow the Notes page 2. need to make two points, and D, that are equidistant from E and F that were produced from different sized radii. E D 2. onstruct perpendicular bisectors to divide QD into four congruent segments. F 1) With compass set longer than 1 2 QD, construct a Q Y X Z D perpendicular bisector. Label the intersection X. 2) onstruct a perpendicular bisector of QX. Label the intersection Y. 3) onstruct a perpendicular bisector of XD. Label the intersection Z. QY = YX = XZ = ZD 7. onstruct perpendicular bisectors of each side of LI. (Make your lines long!) nything interesting happen? They all intersect in one point. L I Next page please! S. Stirling Page 4 of 16
5 h 3 Worksheets S15 KEY LEVEL 2 Name EXERISES Lesson 3.2 Review Problems Page 148 Exercises #12. Make sure you can state the conjectures (properties) you are using a = 50, b = 130, c = 50, d = 130, e = 50, f = 50, g = 130, h = 130, k = 155, m = 115, n = 65 Page 153 # F 16. E D 20. Page 158 #13 show your table, and #16. Write your answers below. #13 Rectangle, n n 35 alc. Value (1)(2) (3)(3) (5)(4) (7)(5) (9)(6) (11)(7) (2 n 1)(n + 1) (69)(36) # of shaded triangles (2 n 1)(n + 1) 2484 #16 Sketch D and EF D. S. Stirling Page 5 of 16
6 h 3 Worksheets S15 KEY LEVEL 2 Name 3.3 onstructing Perpendiculars to a Line Warm up: () You are standing at point and need to run to hurch Hill Road as quickly as possible. How would you determine the shortest distance to the road? Try some different measures and use centimeters, cm, for convenience. Draw them in the figure below. What geometric figure will give you the shortest distance from point to the line (road)? X The shortest distance from the point to the line must be measured along the perpendicular segment from the point to the line. So the shortest distance is X = 2.4 cm. ll of the other distances are longer than X. () How could you measure the distance from point to each of the sides of DP? Think about how you measured your distance from you and the road. (Treat each side of the angle as a road.) Find these distances in cm. D X Y P Need to make a perpendicular from the point to each side. is closer to P Or Y < X. than to D. () Hans, H, is a mountain climber and Jose, J, is a cliff diver. (You can see them on their mountains pictured below.) What would you need to measure to determine Hans altitude at the top of his mountain? Show it in the drawing. How far will Jose dive before hitting the water surface? Show it in the drawing, and you may need to draw some water first. lso, label sea level in each drawing. H J 1.5 cm 1.5 cm S. Stirling Page 6 of 16
7 h 3 Worksheets S15 KEY LEVEL 2 Name EXERISES Lesson 3.3 elow is Page #1 3, 8, 10, 12, 18, Draw perpendiculars from the point P to both sides of IG. Which side is closer to point P? To find the distances from P to each side, you must first draw the perpendiculars to each side through point P (see notes page 3). P is closer to side I, but not by much! I P G 2 & 3. Draw altitudes from all three vertices of each triangle below. Observe where the altitudes are located (inside, outside or on). lso identify the type of triangle (acute, right or obtuse). cute triangle. ll altitudes are inside the triangle. R Right triangle. One altitude is inside; the other two are on the triangle, RG and GT. T G T See notes page 4!!! Obtuse triangle. One altitude is inside; the other two are outside the triangle, so you need to extend the sides. O T S. Stirling Page 7 of 16
8 h 3 Worksheets S15 KEY LEVEL 2 Name 8. Draw an altitude M from the vertex angle of the isosceles right triangle. What do you notice about this segment? Write at least 3 statements! M bisects. M is the midpoint of. M is the perpendicular bisector of. M bisects. M. m = m = 45. m M = m M = 90. M M both are isosceles right triangles. 10. Draw and/or construct a square LE given L as a side. Explain how did it and support your reasoning with properties we ve learned. Need to make right angles at and L and then make L = L = E. Draw E. 3.4 cm L 3.4 cm 3.4 cm E 12. Draw the complement of (without measuring ). Explain how did it and support your reasoning with properties. Use a protractor to draw a 90º angle at So m D + m = 90. Remember to mark 90º angles! S. Stirling Page 8 of 16
9 h 3 Worksheets S15 KEY LEVEL 2 Name 18. Draw a triangle with a 6 cm side and an 8 cm side and the angle between them measuring 40º. Draw a second triangle with a 6 cm side and an 8 cm side and exactly one 40º angle that is not between the two given sides. re the two triangles congruent? Hint: start each triangle with the 8 cm segment on the rays below. Two triangles DEF are possible, because side DF can intersect EF in two different places! Only one triangle is possible. Your triangle should be congruent to. F F D E 20. Draw two triangles. Each should have one side measuring 5 cm and one side measuring 7 cm, but they should not be congruent. Start with the 7 cm segments. Many different triangles are possible with only two given sides. S. Stirling Page 9 of 16
10 h 3 Worksheets S15 KEY LEVEL 2 Name EXERISES Lesson 3.4 elow is Page #6 8, Draw and/or construct an isosceles right triangle with z the length of each of the two legs. z 1) Make a 90º angle at either endpoint, I made m = 90. 2) Either use a compass or a ruler to measure length = z. Make sides of, the legs of, equal length z. Label the intersections and. 3) Draw. 7. Draw and/or construct RP with angle bisector R and the perpendicular bisector of RP. Place your answer on the ray below. P R R 6.6 cm P 1) With a compass, duplicate RP as on Notes page 1. You cannot locate point without a compass! 2) Measure 26 m RP =, and bisect it. 3) Find the midpoint of RP and draw the perpendicular bisector. RP Note: since is scalene, is not the midpoint of P and the perpendicular bisector does not pass through. 8. Draw and/or construct MSE with angle bisector S and altitude S. Place your answer on the ray below. 1) With a protractor, duplicate m M = 29. M M M 3.7 cm 29º 5.7 cm E S 2) With a compass or a ruler, duplicate MS and ME. 3) Measure m MSE = 38, and bisect it. 4) With a protractor, draw altitude S. You will need to extend side ME first because MES is obtuse! S. Stirling Page 10 of 16
11 h 3 Worksheets S15 KEY LEVEL 2 Name 12. onstruct a linear pair of angles (that are not congruent). arefully bisect each angle in the linear pair. What do you notice about the two angle bisectors? an you make a conjecture? an you prove that it is always true? The angle bisectors of a linear pair of angles will be perpendicular (or will form D X y y x x Y EXERISES Lesson 3.4 Review Problems Do page 162 #14 16 Put the info. into the drawings! Must use algebra to solve!. lso do #19 & Given that the lines are parallel. Find y. 15. If E bisects R and m R = 84, find m R. a 90 angle). Prove: Label equal angles x and y. y + y + x + x = 180 form a straight angle. 2 y + 2x = 180 simplify y + x = 90 divide both sides by 2. So X Y. 68 x 55º y 110 5x 10 55º 55º 70º 42º E If parallel, alternate interior angles =. 68 x = 5x = 6x x = 13 If parallel, alternate interior angles =. ( ) = 55 55i 2 = 110 = y Or linear pairs supp = 70 and If parallel, Same side interior angles supp y = = 4x º 7x º R ngle bisector ( x ) = 84 4x + 18 = 42 4x = 24 x = 6 ( ) m R = = 46 S. Stirling Page 11 of 16
12 h 3 Worksheets S15 KEY LEVEL 2 Name 16. Given X bisects largest,, or? 66º 6x Which angle is 7x 3 32º 57 5x 32º 8x º X ngle bisector (congruent angles) 7x 3 = 57 5x 12x = 60 x = 5 m = = 66 ( ) ( ) ( ) m = = 64 m = = 50 Largest. 19. ccurate size! 20. ccurate size! S. Stirling Page 12 of 16
13 h 3 Worksheets S15 KEY LEVEL 2 Name EXERISES Lesson 3.5 & 3.6 Page #1, 2, 4, 5, 17; Page 172 #6 On a separate sheet of paper: Page 165 #14, 15; Page 173 Review #15, Draw a line parallel to n through P using alternate interior angles. Label what you measured and state the property you used. Various answers, but the alternate interior angles need to be labeled as equal. 2. Draw a line parallel to n through P using corresponding angles. Label what you measured and state the property you used. Various answers, but the corresponding angles need to be labeled as equal. n P n P 4. Draw and/or construct a rhombus with x as the length of each side and as one of the acute angles. Place your answer on the ray below. x 1) Use a protractor to draw 35 2) Either use a compass or a ruler to measure length = x. Make sides of equal length x. m =. 3) With a compass set to length x, locate the intersection of the other two congruent sides. 5. Draw and/or construct trapezoid TRP with TR and P as the two parallel sides and with P as the distance between them. (There are many solutions.) Place your answer on the ray below. T R Y P 1) Either use a compass or a ruler to measure length of TR and duplicate it. 2) Draw a perpendicular line anywhere on TR. Make XY = 4.3 and draw a perpendicular line at Y. 3) Draw P anywhere on this line and draw the two remaining sides of TRP. X S. Stirling Page 13 of 16
14 h 3 Worksheets S15 KEY LEVEL 2 Name 3.5 Page 165 Review Exercise #17 k = = Vertical angles m = = Vertical angles q = = 59 a = 72, b = 108, c = 108, d = 108, e = 72, f = 108, g = 108, h = 72, j = 90, k = 18, l = 90, m = 54, n = 62, p = 62, q = 59, r = 118 Page 172 # 6. Draw and/or construct isosceles triangle T with perimeter y and length of the base equal to x. Place your answer on the ray below. y X Y T x 1) Use a compass or a ruler to measure length x = and subtract it from Y. lso construct on the given ray. 2) Since y represents the perimeter of the isosceles triangle, use a compass or a ruler to bisect Y. The resulting segments, =, are the X XY lengths of the remaining sides of the triangle, T and T. 3) Use a compass, set to X or XY to construct the two sides T and T. S. Stirling Page 14 of 16
15 h 3 Worksheets S15 KEY LEVEL 2 Name Review Problems Page 165 #14, 15; Page 173 Review #15, 16 Page 165 #14 Sketch trapezoid ZOID with ZO ID, point T the midpoint of OI and point R the midpoint of ZD. Sketch TR. Page 165 #15 Draw rhombus ROM with m R = 60 and diagonal O. Page 173 #15 If a polygon has 500 diagonals from each vertex, how many sides does it have? 500 = n = n Page 173 #16. Must use actual measures! Draw parallelogram RE so that = 5.5 cm, E = 3.2 cm and m = 110. S. Stirling Page 15 of 16
16 h 3 Worksheets S15 KEY LEVEL 2 Name 3.8 Page 190 Review Exercise #14 h = = = n = = a = 128, b = 52, c = 128, d = 128, e = 52, f = 128, g = 52, h = 38, k = 52, m = 38, n = 71, p = 38 3.R Page Review Exercise #62 & a = 38, b = 38, c = 142, d = 38, e = 50, f = 65, g = 106, h = f = = One possible explanation: Since linear pairs are supplementary m FD = 30. m D = 30 because D and alternate interior angles =. ut its vertical angle has a measure of 26º. This is a contradiction! S. Stirling Page 16 of 16
Lesson 3.1 Duplicating Segments and Angles
Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each
More informationDuplicating Segments and Angles
CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty
More information*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.
Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review
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 informationSum of the interior angles of a nsided Polygon = (n2) 180
5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a nsided Polygon = (n2) 180 What you need to know: How to use the formula
More informationGEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!
GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
More informationUnit 3: Triangle Bisectors and Quadrilaterals
Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties
More informationGeometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24
Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: ctivity 24 esources: Springoard Geometry Unit Overview In this unit, students will study formal definitions of basic figures,
More informationChapter 1: Essentials of Geometry
Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,
More informationStudent Name: Teacher: Date: District: MiamiDade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1
Student Name: Teacher: Date: District: MiamiDade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the
More informationLesson 7: Drawing Parallelograms
Student Outcomes Students use a protractor, ruler, and setsquare to draw parallelograms based on given conditions. Lesson Notes In Lesson 6, students drew a series of figures (e.g., complementary 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 informationGEOMETRY FINAL EXAM REVIEW
GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.
More informationUnit 6 Grade 7 Geometry
Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson
More informationLesson 2: Circles, Chords, Diameters, and Their Relationships
Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct
More informationSelected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
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 informationCongruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key
Instruction Goal: To provide opportunities for students to develop concepts and skills related to identifying and constructing angle bisectors, perpendicular bisectors, medians, altitudes, incenters, circumcenters,
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More informationGEOMETRY. Constructions OBJECTIVE #: G.CO.12
GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
More information55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.
Geometry Core Semester 1 Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit
More informationAlgebra 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 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 informationGeometry Chapter 5 Relationships Within Triangles
Objectives: Section 5.1 Section 5.2 Section 5.3 Section 5.4 Section 5.5 To use properties of midsegments to solve problems. To use properties of perpendicular bisectors and angle bisectors. To identify
More informationGrade 4  Module 4: Angle Measure and Plane Figures
Grade 4  Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles
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 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 informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
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 informationUnit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period
Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,
More informationM 1312 Section Trapezoids
M 1312 Section 4.4 1 Trapezoids Definition: trapezoid is a quadrilateral with exactly two parallel sides. Parts of a trapezoid: Base Leg Leg Leg Base Base Base Leg Isosceles Trapezoid: Every trapezoid
More informationA geometric construction is a drawing of geometric shapes using a compass and a straightedge.
Geometric Construction Notes A geometric construction is a drawing of geometric shapes using a compass and a straightedge. When performing a geometric construction, only a compass (with a pencil) and a
More informationA summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:
summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of midpoint and segment bisector M If a line intersects another line segment
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 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 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 informationSeattle Public Schools KEY to Review Questions for the Washington State Geometry End of Course Exam
Seattle Public Schools KEY to Review Questions for the Washington State Geometry End of ourse Exam 1) Which term best defines the type of reasoning used below? bdul broke out in hives the last four times
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 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 informationThe Triangle and its Properties
THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter 6 6.1 INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three
More informationInscribed Angle Theorem and Its Applications
: Student Outcomes Prove the inscribed angle theorem: The measure of a central angle is twice the measure of any inscribed angle that intercepts the same arc as the central angle. Recognize and use different
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 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 informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More informationGeometry Chapter 1 Vocabulary. coordinate  The real number that corresponds to a point on a line.
Chapter 1 Vocabulary coordinate  The real number that corresponds to a point on a line. point  Has no dimension. It is usually represented by a small dot. bisect  To divide into two congruent parts.
More informationLesson 1.1 Building Blocks of Geometry
Lesson 1.1 Building Blocks of Geometry For Exercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q 2. NQ. 3. nother name for NS is. 4. S is the of SQ. 5. is the midpoint of. 6. NS.
More information0810ge. Geometry Regents Exam 0810
0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More information5.1 Midsegment Theorem and Coordinate Proof
5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle  A midsegment of a triangle is a segment that connects
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 informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationUnit 2  Triangles. Equilateral Triangles
Equilateral Triangles Unit 2  Triangles Equilateral Triangles Overview: Objective: In this activity participants discover properties of equilateral triangles using properties of symmetry. TExES Mathematics
More informationChapter 5: Relationships within Triangles
Name: Chapter 5: Relationships within Triangles Guided Notes Geometry Fall Semester CH. 5 Guided Notes, page 2 5.1 Midsegment Theorem and Coordinate Proof Term Definition Example midsegment of a triangle
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 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 informationPerimeter and area formulas for common geometric figures:
Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,
More informationThe Geometry of Piles of Salt Thinking Deeply About Simple Things
The Geometry of Piles of Salt Thinking Deeply About Simple Things PCMI SSTP Tuesday, July 15 th, 2008 By Troy Jones Willowcreek Middle School Important Terms (the word line may be replaced by the word
More informationVocabulary List Geometry Altitude the perpendicular distance from the vertex to the opposite side of the figure (base)
GEOMETRY Vocabulary List Geometry Altitude the perpendicular distance from the vertex to the opposite side of the figure (base) Face one of the polygons of a solid figure Diagonal a line segment that
More informationOverview of Geometry Map Project
Overview of Geometry Map Project The goal: To demonstrate your understanding of geometric vocabulary, you will be designing and drawing a town map that incorporates many geometric key terms. The project
More informationABC is the triangle with vertices at points A, B and C
Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry  symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the
More informationSOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses
CHAPTER SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY For the review sessions, I will try to post some of the solved homework since I find that at this age both taking notes and proofs are still a burgeoning
More information7. 6 Justifying Constructions
31 7. 6 Justifying Constructions A Solidify Understanding Task CC BY THOR https://flic.kr/p/9qkxv Compass and straightedge constructions can be justified using such tools as: the definitions and properties
More informationQuadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid
Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, June 19, :15 a.m. to 12:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 19, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
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 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 informationEXPECTED BACKGROUND KNOWLEDGE
MOUL  3 oncurrent Lines 12 ONURRNT LINS You have already learnt about concurrent lines, in the lesson on lines and angles. You have also studied about triangles and some special lines, i.e., medians,
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 information(n = # of sides) One interior angle:
6.1 What is a Polygon? Regular Polygon Polygon Formulas: (n = # of sides) One interior angle: 180(n 2) n Sum of the interior angles of a polygon = 180 (n  2) Sum of the exterior angles of a polygon =
More informationFind the measure of each numbered angle, and name the theorems that justify your work.
Find the measure of each numbered angle, and name the theorems that justify your work. 1. The angles 2 and 3 are complementary, or adjacent angles that form a right angle. So, m 2 + m 3 = 90. Substitute.
More informationGeometry Review Flash Cards
point is like a star in the night sky. However, unlike stars, geometric points have no size. Think of them as being so small that they take up zero amount of space. point may be represented by a dot on
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 informationGeometry, Final Review Packet
Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a
More informationGrade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013
Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is
More information2. Construct the 3 medians, 3 altitudes, 3 perpendicular bisectors, and 3 angle bisector for each type of triangle
Using a compass and straight edge (ruler) construct the angle bisectors, perpendicular bisectors, altitudes, and medians for 4 different triangles; a, Isosceles Triangle, Scalene Triangle, and an. The
More informationDate: Period: Symmetry
Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into
More informationSession 4 Angle Measurement
Key Terms in This Session Session 4 Angle Measurement New in This Session acute angle adjacent angles central angle complementary angles congruent angles exterior angle interior (vertex) angle irregular
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 information2.1. Inductive Reasoning EXAMPLE A
CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers
More information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More informationCenters of Triangles Learning Task. Unit 3
Centers of Triangles Learning Task Unit 3 Course Mathematics I: Algebra, Geometry, Statistics Overview This task provides a guided discovery and investigation of the points of concurrency in triangles.
More informationConstructing Symmetrical Shapes
07NEM5WBAnsCH07 7/20/04 4:36 PM Page 62 1 Constructing Symmetrical Shapes 1 Construct 2D shapes with one line of symmetry A line of symmetry may be horizontal or vertical 2 a) Use symmetry to complete
More information65 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.
ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram
More informationGeometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.
Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know
More informationUnit 6 Grade 7 Geometry
Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson
More informationGiven: ABCD is a rhombus. Prove: ABCD is a parallelogram.
Given: is a rhombus. Prove: is a parallelogram. 1. &. 1. Property of a rhombus. 2.. 2. Reflexive axiom. 3.. 3. SSS. + o ( + ) =180 4.. 4. Interior angle sum for a triangle. 5.. 5. PT + o ( + ) =180 6..
More information1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.
Quadrilaterals  Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals  Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,
More informationSection 91. Basic Terms: Tangents, Arcs and Chords Homework Pages 330331: 118
Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,
More informationUse the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. 1. measures less than By the Exterior Angle Inequality Theorem, the exterior angle ( ) is larger than
More informationSec 1.1 CC Geometry  Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB.
Sec 1.1 CC Geometry  Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have
More informationNotes on Perp. Bisectors & Circumcenters  Page 1
Notes on Perp. isectors & ircumcenters  Page 1 Name perpendicular bisector of a triangle is a line, ray, or segment that intersects a side of a triangle at a 90 angle and at its midpoint. onsider to the
More informationGeometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths Makes
More informationIsosceles triangles. Key Words: Isosceles triangle, midpoint, median, angle bisectors, perpendicular bisectors
Isosceles triangles Lesson Summary: Students will investigate the properties of isosceles triangles. Angle bisectors, perpendicular bisectors, midpoints, and medians are also examined in this lesson. A
More informationConjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence  a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
More informationThis is a tentative schedule, date may change. Please be sure to write down homework assignments daily.
Mon Tue Wed Thu Fri Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Introductions, Expectations, Course Outline and Carnegie Review summer packet Topic: (11) Points, Lines, & Planes Topic: (12) Segment Measure Quiz
More informationPOTENTIAL REASONS: Definition of Congruence:
Sec 6 CC Geometry Triangle Pros Name: POTENTIAL REASONS: Definition Congruence: Having the exact same size and shape and there by having the exact same measures. Definition Midpoint: The point that divides
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 informationAreas of Rectangles and Parallelograms
CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson you will Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover
More information114 Areas of Regular Polygons and Composite Figures
1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,
More informationParallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.
CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes
More information