Applications for Triangles
|
|
|
- Norah Hunter
- 7 years ago
- Views:
Transcription
1 Not drawn to scale Applications for Triangles in. 40 in. 33 in in in in in in in in. 2 none of these Find the area of a parallelogram with the given vertices. 3. P(1, 3), Q(3, 3), R(7, 8), S(9, 8) 10 units 2 5 units 2 20 units 2 none of these 4. An isosceles triangle has area of 110 ft 2. If the base is 14 ft, what is the length of the legs? Round your answer to the nearest tenth. 21 ft 17.2 ft 14.8 ft ft 5. A fly lands at random at a point on the gri Find the probability of the fly landing on the figure. 6. Find the area of the rhombus. Leave your answer in simplest radical form
2 P 18 Q 7. In trapezoid PQRS,.. Find the area of PQRS. Leave your answer in simplified radical form. 8. Given the regular polygon, find the measure of each numbered angle S R Given the regular hexagon, find the measure of each numbered angle Given a regular hexagon, find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the polygon. 40 ; ; ; ; The area of a regular hexagon is 35 in. 2. Find the length of a side. Round your answer to the nearest tenth. 3.7 in. 4.8 in. 6.4 in in. 12. Find the area of a regular hexagon with side length of 8 m. Round your answer to the nearest tenth m m m m Find the area of an equilateral triangle with side Find the area of the regular polygon. Round your answer to the nearest tenth.
3 13.07 in. 10 in in in in in You are planning to use a ceramic tile design in your new bathroom. The tiles are blue and white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 7 centimeters, what will be the exact area of each hexagonal shape? 7 cm 73.5 cm 2 98 cm 2 21 cm cm Find the area of an equilateral triangle with radius 8 m. Leave your answer in simplest radical form. 96 m m 2 18 m 2 12 m A regular hexagon has a perimeter of 150 m. Find its are Leave your answer in simplest radical form m m m m 2 2 The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. 18. The area of a regular octagon is 35 cm. What is the area of a regular octagon with sides three times as large? 315 cm 225 cm 175 cm 105 cm Find the area of the regular polygon. Give the answer to the nearest tenth. 19. pentagon with side 10 cm cm 20. hexagon with side 8 yd yd 34.4 cm 12 yd cm 41.6 yd 172 cm yd
4 21. decagon with side 4 cm cm cm cm cm 22. dodecagon with perimeter 108 cm cm cm cm cm 23. pentagon with radius 8 m m m 30.4 m m 24. hexagon with radius 5 in in in in in. 25. The Ruffs are planning to buy an above-ground swimming pool shaped as a regular octagon. The radius of the octagon is 9 feet. To the nearest tenth, find the area of the surface of the water in the pool ft ft 94.8 ft ft 26. Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale. 15 cm??? 9 cm cm 63.4 cm 23.1 cm cm 4.7 m??? 6.1 m 10.5 m 9.8 m 19.6 m 21.0 m 28. A gardener needs to cultivate a triangular plot of lan One angle of the garden is 47, and two sides adjacent to the angle are 77 feet and 76 feet. To the nearest tenth, what is the area of the plot of land? ft ft ft ft 29. A park in a subdivision is triangular-shape Two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58. To the nearest unit, find the area of the park in square yards.
5 32,557 yd 14,470 yd 28,940 yd 43,410 yd 30. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35. To the nearest hundredth, find the search are 2.08 mi 2.97 mi 1.04 mi 1.49 mi 31. Two triangles each have adjacent sides of length 120 feet and 180 feet. The first triangle has an angle between the two sides of 40, while the second triangle has an angle between the two sides of 60. What is the approximate difference between the areas of the two triangles? 4822 ft 2873 ft 5746 ft 2411 ft
6 32. Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. Find the measure of each central angle in the circle graph. Sleeping Eating ; ; ; ; Name the minor arc and find its measure. A D C ) 115 B arc ADB; 30 arc AB; 115 arc ADB; 245 arc AB; Name the major arc and find its measure. A D C )50 B
7 arc ADB; 50 arc AB; 50 arc ADB; 310 arc AB; Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a circle. Leave your answer in terms of. 36. A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 35 cm. To the nearest tenth, what is the area of the wheel? cm cm cm cm 2 Find the area of the circle. Leave your answer in terms of. 37. The figure represents the overhead view of a deck surrounding a hot tu What is the area of the deck? Round to the nearest tenth m m m m Find the area of the shaded portion of the figure. Dimensions are in feet. Leave your answer in terms of π.
8 none of these 39. Find the area of the figure to the nearest tenth in in in in A 4-ft-by-5-ft dock is anchored in the middle of a lake. The bow of a boat is tied to a corner of the dock with a 5-ft rope as shown in the picture. Find the area of the region in which the bow of the boat can travel. Round your answer to the nearest foot. Not drawn to scale 60 ft 2 58 ft 2 81 ft 2 none of these 41. Find the exact area of the shaded region.
9 none of these 42. Find the area of the shaded region. Leave your answer in terms of and in simplest radical form. none of these 43. What is the probability that a point chosen at random on the grid will lie in the unshaded region?
10 44. The radius of the bull s-eye of the dartboard is 8 inches. The radius of each concentric circle is 8 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, what is the probability that the dart will hit in area C? A B C D 45. Find the probability that a point chosen at random will lie in the shaded are
11 46. A circular dartboard has a radius of 2 meters and a red circle in the center. Assume you hit the target at a random point. For what radius of the red center region does P(hitting red) = 0.6? 77 m 1.2 m 1.55 cm 1.32 m 47. The regular polygon has radius 9 m. Find each angle measure to the nearest tenth of a degree, each linear measure to the nearest tenth of a meter, and the square measure to the nearest square meter. G H F E O A X B D C OX AB e. the perimeter f. the area Essay 48. Find the area of a regular hexagon with sides 2 cm long. Leave your answer in simplest radical form. Use your answer from part (a) to find the area of a regular hexagon of side length An outdoor deck for a new restaurant forms a square with radius 30 feet. Draw and label a diagram of the deck. Explain your diagram. Find the perimeter of the deck. Explain your method for finding the perimeter. Find the area of the deck. Explain your method for finding the are Show a method for finding the area of the deck that is different from the method you used in part (c). 50. Use this triangle. 7 in.??????
12 Find the length of the hypotenuse using the special relationships for a triangle. Explain the relationships. Write the exact value for sin 45 as a fraction in simplest form. Use the formula for the area of a triangle given SAS to find the area of the triangle. Explain your steps. Use a different method to find the area of the triangle. Explain your steps. 51. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. About how much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim? Show your work. 52. Jason designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron used to make the structure. Round the answer to the nearest meter.
13 Applications Answer Section MULTIPLE CHOICE 1) A 2) B 3) A 4) B 5) B 6) D 7) A 8)B 9) C 10) B 11) A 12) B 13) A 14) D 15) A 16) B 17) B 18 A 19) D 20)D 21) A 22) B 23) B 24) C 25) D 26) B 27) A 28) B 29) B 30) C 31) D 32 A 33) B 34 C 35 A 36)B 37) B 38 C 39) A 40 A 41)B 42)C 43)A 44 B 45 A 46) C 47. ANS: m 6.8 m e m f. 229 m 48. ANS: [4] Answers may vary. Sample: The central angle of one of the triangles in the hexagon is. The altitude of the triangle is because it is a - - right triangle.
![39) A 40 A 41)B 42)C 43)A 44 B 45 A 46) C 47. ANS: 22.5 45 8.3 m 6.8 m e. 55.1 m f. 229 m 48. ANS: [4] Answers may vary.](/docs-images/47/21053060/images/page_13.jpg "Sample: The central angle of one of the triangles in the hexagon is.")
14 ??? 2 cm??? 1 cm The area of the hexagon is therefore. Because regular hexagons are similar, their areas will be proportional to the square of their similarity ratio.. cm ANS: [4] 30 ft a x The radius of the square from its center to a corner is 30 feet. A triangle can be formed where x is half the side length and a is the apothem. The triangle in the diagram is a triangle. The hypotenuse 30 is x and a and a = x. To find the value of x, or a, write and solve an equation. 30 = x Write an equation. = Divide each side by x Use a calculator. So, x = a 21.2 and the perimeter is about 2(21.2)(4) feet, or feet. Now, use the formula for the area of a regular polygon. A =
15 = Substitute. = Simplify. The area of the deck is about 1798 square feet. Another way to find the area is to use the formula for the area of a square. The length of the side of the deck is 2(21.2), or The area of the deck is about 1798 square feet. 50. ANS: [4] In a triangle, the length of the hypotenuse is the length of the short leg times, so the length of the hypotenuse is 7 in. The exact value of sin 45 is = =. Area of a triangle = = b = 7, c = 7, A = 45 = Simplify. = 24.5 The area of the triangle is 24.5 in.. Another formula for the area of a triangle if the base length and height are known is. For this triangle, b = 7 and h = 7 since they are the legs of a right triangle. A = = b = 7, h = 7 = Simplify. = 24.5 The area of the triangle is 24.5 in ANS
![ANS: [4] In a 45-45 -90 triangle, the length of the hypotenuse is the length of the short leg times, so the length of the hypotenuse is 7 in. The exact value of sin 45 is = =.](/docs-images/47/21053060/images/page_15.jpg "Area of a triangle = = b = 7, c = 7, A = 45 = Simplify. = 24.5 The area of the triangle is 24.5 in.. Another formula for the area of a triangle if the base length and height are known is.")
16 [4] Answers may vary. Sample: If a basketball has a circumference of 30, then its diameter is. If the ball goes in exactly in the center of the rim, then there is a total of ( ) inches or inches on both sides of the ball. Therefore, there is half of this distance, or about 4.2 inches, between the ball and the rim. [3] correct methods used, but with a computational error [2] error in method [1] correct answer with no work shown 52. ANS: [4] Answers may vary. Sample: The total length of wrought iron used is the sum of the outer circumference plus the inner circumference plus the eleven segments. The length of wrought iron used is approximately 59 meters.
PERIMETER 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
Chapter 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
SA 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.
Postulate 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
Teacher 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
Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite
2006 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
Chapter 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
GEOMETRY B: CIRCLE TEST PRACTICE
Class: Date: GEOMETRY B: CIRCLE TEST PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the measures of the indicated angles. Which statement
Geometry 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
Unit 7 Circles. Vocabulary and Formulas for Circles:
ccelerated G Unit 7 ircles Name & ate Vocabulary and Formulas for ircles: irections: onsider 1) Find the circumference of the circle. to answer the following questions. Exact: pproximate: 2) Find the area
2nd 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
MCA Formula Review Packet
MCA Formula Review Packet 1 3 4 5 6 7 The MCA-II / BHS Math Plan Page 1 of 15 Copyright 005 by Claude Paradis 8 9 10 1 11 13 14 15 16 17 18 19 0 1 3 4 5 6 7 30 8 9 The MCA-II / BHS Math Plan Page of 15
9 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
Geometry 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
Area 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
of 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
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:
Chapter 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
Perimeter 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
Area. 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.
Calculating 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
Area 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
Section 7.1 Solving Right Triangles
Section 7.1 Solving Right Triangles Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45,
Course 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
Tallahassee 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
43 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
YOU 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
Geometry 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
Pizza! Pizza! Assessment
Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the
Characteristics 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.
How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
CSU 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
Solids. 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
MULTIPLE 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
Area is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
Cumulative 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
MEASUREMENTS. 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
FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication
FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby
Lesson 21. Circles. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine
Show 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
12-1 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
GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
SURFACE 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
Quick 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
Perimeter, Area, and Volume
Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
Area 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
56 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
Pythagorean Theorem: 9. x 2 2
Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2
Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain
AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent
Area 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
MATH 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
The 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
TEKS 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
All I Ever Wanted to Know About Circles
Parts of the Circle: All I Ever Wanted to Know About Circles 1. 2. 3. Important Circle Vocabulary: CIRCLE- the set off all points that are the distance from a given point called the CENTER- the given from
Conjectures 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:
Angles 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,
Geometry Final Exam Review Worksheet
Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.
Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)
Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.
7 th Grade Study guide IV Partial Remember to practice the constructions that are not part of this guide.
7 th Grade Study guide IV Partial Remember to practice the constructions that are not part of this guide. 1. Which figure shows one point? a. S R c. D C b. Q d. F G 2. Which name describes the line? G
Parallel 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
How To Solve The Pythagorean Triangle
Name Period CHAPTER 9 Right Triangles and Trigonometry Section 9.1 Similar right Triangles Objectives: Solve problems involving similar right triangles. Use a geometric mean to solve problems. Ex. 1 Use
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
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
Geometry 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
Conjectures. 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
GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book
GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18
1-6 Two-Dimensional Figures. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
Stop signs are constructed in the shape of a polygon with 8 sides of equal length The polygon has 8 sides A polygon with 8 sides is an octagon All sides of the polygon are congruent and all angles are
Grade 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
Shape 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
Grade 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
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Thursday, June 14, 2012 1:15 to 4:15 p.m.
INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, June 14, 2012 1:15 to 4:15 p.m., only Student Name: School Name: Print your name
Mental Questions. Day 1. 1. What number is five cubed? 2. A circle has radius r. What is the formula for the area of the circle?
Mental Questions 1. What number is five cubed? KS3 MATHEMATICS 10 4 10 Level 8 Questions Day 1 2. A circle has radius r. What is the formula for the area of the circle? 3. Jenny and Mark share some money
Perimeter. 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
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Thursday, August 16, 2012 8:30 to 11:30 a.m.
INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name
16 Circles and Cylinders
16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two
Session 7 Circles and Pi (π)
Key Terms in This Session Session 7 Circles and Pi (π) Previously Introduced accuracy area precision scale factor similar figures New in This Session circumference diameter irrational number perimeter
12 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
Areas of Circles and Sectors. GO for Help
-7 What You ll Learn To find the areas of circles, sectors, and segments of circles... nd Why To compare the area of different-size pizzas, as in Example reas of ircles and Sectors heck Skills You ll Need
UNIT H1 Angles and Symmetry Activities
UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)
WEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet - 36 inches. 1 Rod 5 1/2 yards - 16 1/2 feet
WEIGHTS AND MEASURES Linear Measure 1 Foot12 inches 1 Yard 3 feet - 36 inches 1 Rod 5 1/2 yards - 16 1/2 feet 1 Furlong 40 rods - 220 yards - 660 feet 1 Mile 8 furlongs - 320 rods - 1,760 yards 5,280 feet
CIRCUMFERENCE 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
Grade 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
Tangent Properties. Line m is a tangent to circle O. Point T is the point of tangency.
CONDENSED LESSON 6.1 Tangent Properties In this lesson you will Review terms associated with circles Discover how a tangent to a circle and the radius to the point of tangency are related Make a conjecture
Geometry 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
Circumference of a Circle
Circumference of a Circle A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If
Lesson 9.1 The Theorem of Pythagoras
Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius
MENSURATION. 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
12 Surface Area and Volume
CHAPTER 12 Surface Area and Volume Chapter Outline 12.1 EXPLORING SOLIDS 12.2 SURFACE AREA OF PRISMS AND CYLINDERS 12.3 SURFACE AREA OF PYRAMIDS AND CONES 12.4 VOLUME OF PRISMS AND CYLINDERS 12.5 VOLUME
Area 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
B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3
45 Volume Surface area measures the area of the two-dimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space
Target 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
Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find
MATH 100 PRACTICE FINAL EXAM
MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number
GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement
GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4
Algebra 1 End-of-Course Assessment Sample Questions Regular Print Paper-Based Accommodation
Algebra 1 End-of-Course Assessment Sample Questions Regular Print Paper-Based Accommodation The intent of these sample test materials is to orient teachers and students to the types of questions on the
Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: ID: A Q3 Geometry Review Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the image of each figure under a translation by the given
11.3 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
Scope 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
Lesson 1: Introducing Circles
IRLES N VOLUME Lesson 1: Introducing ircles ommon ore Georgia Performance Standards M9 12.G..1 M9 12.G..2 Essential Questions 1. Why are all circles similar? 2. What are the relationships among inscribed
Circumference CHAPTER. www.ck12.org 1
www.ck12.org 1 CHAPTER 1 Circumference Here you ll learn how to find the distance around, or the circumference of, a circle. What if you were given the radius or diameter of a circle? How could you find