1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection?

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection?"

Transcription

1 Student Name: Teacher: Date: District: Description: Miami-Dade County Public Schools Geometry Topic 7: 3-Dimensional Shapes 1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection? square triangle parabola straight line 2. Which phrase describes a possible intersection of a plane with a double cone? two lines two points two circles two ellipses 3. The volume of the given cylinder is cubic units. Which is closest to the radius, r, of the base in units?

2 4. Sam works at an ice cream store and sells ice cream cookie sandwiches that are 0.25 inches thick and have a 3 inch diameter. They are filled with ice cream that is 0.75 inches high and reaches to 0.25 inches away from the edge of the cookie. What is the volume of each ice cream sandwich? 3.67 cubic inches 5.45 cubic inches 7.21 cubic inches 7.98 cubic inches 5. Jordan wants to prove the formula for the volume of the pyramid below by inserting the pyramid into a rectangular prism. Into which rectangular prism should Jordan insert the pyramid?

3 6. Two vases have the same height but are shaped differently as shown below. How could the vases be sliced to use Cavalieri's principle to show that their volumes are equivalent?

4 7. Consider this proof: Which reason could be used to justify Statement 3 in this proof? subtraction property of equality substitution property of equality definition of supplementary definition of complementary 8. A truck hauled 136 cubic feet of sand to a construction site. The sand is dumped into a cone-shaped pile 6 feet in height. What is the approximate diameter of the pile of sand, in feet? Stan wants to double the volume of the jar shown below.

5 Which operation would accomplish this? doubling the height doubling the diameter doubling the height and diameter halving the diameter and quadrupling the height 10. Margaret is using a hollow cone and a hollow cylinder to determine how the volume of a cone relates to the volume of a cylinder. The heights and diameters of the bases of the cone and the cylinder are equal. Margaret fills the cone completely with water and then pours the water into the cylinder. What will she find? The water fills of the cylinder. The water fills of the cylinder. The water will fill the cylinder to the top. The water fills of the cylinder. 11. Given: PQRS is a parallelogram; S, P, and T are collinear. Prove: 1 4. Statements Reasons 1. PQRS is a parallelogram; S, P, and T 1. Given are collinear Definition of a parallelogram Parallel lines cut by a transversal form congruent corresponding angles Definition of a parallelogram ? Transitive property of congruence Which reason could be used to justify Statement 5? Angles that are supplements of the same angle are congruent to each other. Parallel lines cut by a transversal form congruent alternate interior angles. Parallel lines cut by a transversal form congruent corresponding angles. Intersecting lines form congruent vertical angles.

6 12. A food company currently sells tomato juice in a cylindrical container with a diameter of 6 centimeters (cm) and a height of 10 cm. The company's marketing team suggests there would be better sales if the container were a cone. What should the diameter of the cone be if the company changes neither the height nor the volume? Round to the nearest cm, if needed Which formula can be used to determine the volume of this 3-dimensional figure?

7 14. Monica lists the steps to prove that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Which statement should Monica write in the blank in step 5? 15. The graph below shows a semicircle with a radius of 2 units. About what line should the semicircle be revolved in order to create a sphere? the line y = 0 the line x = 0 the line x = 2 the line y = 2

8 16. Max is planting four 20 foot tall palm trees alongside his house. Each tree will need a cylindrical hole that is 34 inches in diameter and 28 inches deep to accommodate the roots. His trash hauler will only take away the excess dirt if it is in rectangular bags that are 2 feet by 1.5 feet by four feet. However, Max can only fill the bags one third of the way or they will be too heavy for him to move. How many bags will he have to buy so he can put all the dirt out for pickup? A plane intersects a cylinder without intersecting either of its bases. The plane is not parallel to the bases. What geometric figure will be formed from this intersection? a circle a square an ellipse a line segment 18. A certain cylinder has a height of and a certain square prism has a height of The circular cross section of the cylinder and the square cross section of the prism have the same area. Which equation expresses the relationship of the volume of the cylinder, to the volume of the prism,

9 19. Sam wants to compare the volumes of the cone in Figure 1 and the square pyramid in Figure 3 below. The heights of the cone and the pyramid are equal. The radius of the base of the cone and the length of the base of the pyramid are given in centimeters (cm). When the cone is placed inside the pyramid, the base of the cone touches each edge of the square base of the pyramid at one point, as shown in Figure 2. The volume of the cone is 1884 cubic centimeters. What is the difference in the volume of the pyramid and the volume of the cone, in cubic centimeters? A line segment PQ has endpoint P at and Q at As a result of dilation about the origin, the endpoint of P' has coordinates What are the coordinates of Q'? 21. A rectangle will be rotated about Line L in the figure below. What best describes the three-dimensional object formed by rotating the rectangle about Line L? solid cylinder solid rectangular prism rectangular prism with a square hole down its length cylinder with a cylindrical hole down its length

10 22. The figures shown below all have circular bases with a radius of r units. The four figures have equal heights. Which figures, if any, have equal volumes? I and II; III and IV I and III; II and IV All of the figures have equal volume. No two figures have equal volume. 23. What are the coordinates of if the orgin is the center of dilation and the scale factor is?

11 24. The endpoints of are located at E (-4, -2) and F (2,3). What are the coordinates of point G, which divides such that EG : GF is equal to 1 : 3? (-2.5, -1) (-2.5, -0.75) (-1, 0.5) (0.5, 1.75) 25. The volume of a sphere is cubic inches. If the radius of the sphere is doubled, what is the volume, in cubic inches, of the new sphere?

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

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

More information

Name: Date: Geometry Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Solid Geometry. Name: Teacher: Pd: Name: Date: Geometry 2012-2013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-7 HW: Pgs: 8-10 DAY 2: SWBAT: Calculate the Volume of

More information

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel

More information

Geometry Notes PERIMETER AND AREA

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

More information

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1 Student Name: Teacher: Date: District: Miami-Dade 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 information

Geometry Notes VOLUME AND SURFACE AREA

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

More information

Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd: Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

More information

Area of Parallelograms (pages 546 549)

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

More information

1. 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. 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 information

Algebra Geometry Glossary. 90 angle

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 information

Chapter 1: Essentials of Geometry

Chapter 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 information

Geometry Course Summary Department: Math. Semester 1

Geometry 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 information

Topics Covered on Geometry Placement Exam

Topics 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 information

New York State Student Learning Objective: Regents Geometry

New York State Student Learning Objective: Regents Geometry New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students

More information

Overview Mathematical Practices Congruence

Overview Mathematical Practices Congruence Overview Mathematical Practices Congruence 1. Make sense of problems and persevere in Experiment with transformations in the plane. solving them. Understand congruence in terms of rigid motions. 2. Reason

More information

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warm-up 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

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 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 information

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

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

More information

Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem. Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

More information

Geometry Enduring Understandings Students will understand 1. that all circles are similar.

Geometry Enduring Understandings Students will understand 1. that all circles are similar. High School - Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,

More information

CHAPTER 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.

CHAPTER 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 information

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.

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. 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 information

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.

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. 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 information

How does one make and support a reasonable conclusion regarding a problem? How does what I measure influence how I measure?

How does one make and support a reasonable conclusion regarding a problem? How does what I measure influence how I measure? Middletown Public Schools Mathematics Unit Planning Organizer Subject Mathematics Grade/Course Grade 7 Unit 3 Two and Three Dimensional Geometry Duration 23 instructional days (+4 days reteaching/enrichment)

More information

12-6 Surface Area and Volumes of Spheres. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. SOLUTION: ANSWER: 1017.

12-6 Surface Area and Volumes of Spheres. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. SOLUTION: ANSWER: 1017. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. 3. sphere: area of great circle = 36π yd 2 We know that the area of a great circle is r.. Find 1. Now find the surface area.

More information

12-8 Congruent and Similar Solids

12-8 Congruent and Similar Solids Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. Ratio of radii: Ratio of heights: The ratios of the corresponding measures are

More information

GEOMETRY CONCEPT MAP. Suggested Sequence:

GEOMETRY 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 information

GEOMETRY COMMON CORE STANDARDS

GEOMETRY COMMON CORE STANDARDS 1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,

More information

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units 1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units

More information

FSA Geometry End-of-Course Review Packet. Modeling and Geometry

FSA Geometry End-of-Course Review Packet. Modeling and Geometry FSA Geometry End-of-Course Review Packet Modeling and Geometry MAFS.912.G-MG.1.1 EOC Practice Level 2 Level 3 Level 4 Level 5 uses measures and properties to model and describe a realworld object that

More information

Perimeter, Area, and Volume

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

More information

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

*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 information

Geo - CH10 Practice Test

Geo - CH10 Practice Test Geo - H10 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. lassify the figure. Name the vertices, edges, and base. a. triangular pyramid vertices:,,,,

More information

Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:

Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources: Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard- Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students

More information

12-8 Congruent and Similar Solids

12-8 Congruent and Similar Solids Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 3. Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio

More information

Chapter 8 Geometry We will discuss following concepts in this chapter.

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

More information

SURFACE AREA AND VOLUME

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

More information

Geometry and Measurement

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

More information

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.

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. 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 information

TERMINOLOGY Area: the two dimensional space inside the boundary of a flat object. It is measured in square units.

TERMINOLOGY Area: the two dimensional space inside the boundary of a flat object. It is measured in square units. SESSION 14: MEASUREMENT KEY CONCEPTS: Surface Area of right prisms, cylinders, spheres, right pyramids and right cones Volume of right prisms, cylinders, spheres, right pyramids and right cones the effect

More information

17.1 Cross Sections and Solids of Rotation

17.1 Cross Sections and Solids of Rotation Name Class Date 17.1 Cross Sections and Solids of Rotation Essential Question: What tools can you use to visualize solid figures accurately? Explore G.10.A Identify the shapes of two-dimensional cross-sections

More information

2nd Semester Geometry Final Exam Review

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

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

More information

Geometry, Final Review Packet

Geometry, 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 information

Lesson 17 ~ Volume of Prisms

Lesson 17 ~ Volume of Prisms Lesson 17 ~ Volume of Prisms 1. An octagonal swimming pool has a base area of 42 square meters. The pool is 3 feet deep. Find the volume of the pool. 2. A fish aquarium is a rectangular prism. It is 18

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, June 19, :15 a.m. to 12:15 p.m., only.

The 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 information

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7 Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are 5 6 0 unit cubes in each layer.

More information

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 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 information

chp12review Name: Class: Date: 1. Find the number of vertices, faces, and edges for the figure below.

chp12review Name: Class: Date: 1. Find the number of vertices, faces, and edges for the figure below. Name: Class: Date: chp12review 1. Find the number of vertices, faces, and edges for the figure below. a. 6 vertices, 6 faces, 10 edges b. 5 vertices, 6 faces, 10 edges c. 7 vertices, 7 faces, 11 edges

More information

ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone. 8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

More information

Geometry FSA Mathematics Practice Test Answer Key

Geometry FSA Mathematics Practice Test Answer Key Geometry FSA Mathematics Practice Test Answer Key The purpose of these practice test materials is to orient teachers and students to the types of questions on paper-based FSA tests. By using these materials,

More information

3D Geometry: Chapter Questions

3D Geometry: Chapter Questions 3D Geometry: Chapter Questions 1. What are the similarities and differences between prisms and pyramids? 2. How are polyhedrons named? 3. How do you find the cross-section of 3-Dimensional figures? 4.

More information

2006 Geometry Form A Page 1

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

More information

Area is a measure of how much space is occupied by a figure. 1cm 1cm

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

More information

Honors Geometry Final Exam Study Guide

Honors Geometry Final Exam Study Guide 2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

More information

Study Guide and Review

Study Guide and Review Fill in the blank in each sentence with the vocabulary term that best completes the sentence. 1. A is a flat surface made up of points that extends infinitely in all directions. A plane is a flat surface

More information

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

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

More information

24HourAnswers.com. Online Homework. Focused Exercises for Math SAT. Skill Set 12: Geometry - 2D Figures and 3D Solids

24HourAnswers.com. Online Homework. Focused Exercises for Math SAT. Skill Set 12: Geometry - 2D Figures and 3D Solids 24HourAnsers.com Online Homeork Focused Exercises for Math SAT Skill Set 12: Geometry - 2D Figures and 3D Solids Many of the problems in this exercise set came from The College Board, riters of the SAT

More information

Centroid: The point of intersection of the three medians of a triangle. Centroid

Centroid: 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 information

Geometry Vocabulary. Created by Dani Krejci referencing:

Geometry Vocabulary. Created by Dani Krejci referencing: Geometry Vocabulary Created by Dani Krejci referencing: http://mrsdell.org/geometry/vocabulary.html point An exact location in space, usually represented by a dot. A This is point A. line A straight path

More information

Incoming Frederick Douglass HS Geometry Students

Incoming Frederick Douglass HS Geometry Students Incoming Frederick Douglass HS Geometry Students 2016-2017 Dear FDHS Student, To better prepare you for the upcoming school year, it is the expectation is that all students bring the completed assignment

More information

Section 2.1 Rectangular Coordinate Systems

Section 2.1 Rectangular Coordinate Systems P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

More information

LESSON SUMMARY. Measuring Shapes

LESSON SUMMARY. Measuring Shapes LESSON SUMMARY CXC CSEC MATHEMATICS UNIT SIX: Measurement Lesson 11 Measuring Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 (Some helpful exercises and page numbers are given

More information

Practice: Space Figures and Cross Sections Geometry 11-1

Practice: Space Figures and Cross Sections Geometry 11-1 Practice: Space Figures and Cross Sections Geometry 11-1 Name: Date: Period: Polyhedron * 3D figure whose surfaces are * each polygon is a. * an is a segment where two faces intersect. * a is a point where

More information

Let s find the volume of this cone. Again we can leave our answer in terms of pi or use 3.14 to approximate the answer.

Let s find the volume of this cone. Again we can leave our answer in terms of pi or use 3.14 to approximate the answer. 8.5 Volume of Rounded Objects A basic definition of volume is how much space an object takes up. Since this is a three-dimensional measurement, the unit is usually cubed. For example, we might talk about

More information

Conjectures. Chapter 2. Chapter 3

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

More information

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

VOLUME 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 information

Angles that are between parallel lines, but on opposite sides of a transversal.

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,

More information

Everyday Mathematics. Grade 3 Grade-Level Goals. 3rd Edition. Content Strand: Number and Numeration. Program Goal Content Thread Grade Level Goal

Everyday Mathematics. Grade 3 Grade-Level Goals. 3rd Edition. Content Strand: Number and Numeration. Program Goal Content Thread Grade Level Goal Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation

More information

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.

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

More information

Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice. Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism

More information

CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:

CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name: GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships

More information

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.

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. 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 information

Scope & Sequence MIDDLE SCHOOL

Scope & Sequence MIDDLE SCHOOL Math in Focus is a registered trademark of Times Publishing Limited. Houghton Mifflin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A. 06/13 MS77941n Scope & Sequence MIDDLE SCHOOL

More information

Assessment For The California Mathematics Standards Grade 4

Assessment 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 information

BASIC GEOMETRY GLOSSARY

BASIC GEOMETRY GLOSSARY BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that

More information

Geometry Vocabulary Booklet

Geometry Vocabulary Booklet Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular

More information

12-1 Representations of Three-Dimensional Figures

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

More information

of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent. 2901 Clint Moore Road #319, Boca Raton, FL 33496 Office: (561) 459-2058 Mobile: (949) 510-8153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:

More information

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable. Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the

More information

Practice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Paper

Practice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Paper The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving

More information

Geometry. Higher Mathematics Courses 69. Geometry

Geometry. Higher Mathematics Courses 69. Geometry The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and

More information

Integrated Algebra: Geometry

Integrated Algebra: Geometry Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

More information

UNIT PLAN. Big Idea/Theme: Shapes can be analyzed, described, and related to our physical world.

UNIT PLAN. Big Idea/Theme: Shapes can be analyzed, described, and related to our physical world. UNIT PLAN Grade Level: 2 Unit #: 5 Unit Name: Geometry Big Idea/Theme: Shapes can be analyzed, described, and related to our physical world. Culminating Assessment: Use real world objects from home, create

More information

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

More information

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 4 AREAS AND VOLUMES This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.

More information

In Problems #1 - #4, find the surface area and volume of each prism.

In Problems #1 - #4, find the surface area and volume of each prism. Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

More information

Chapter 4: Area, Perimeter, and Volume. Geometry Assessments

Chapter 4: Area, Perimeter, and Volume. Geometry Assessments Chapter 4: Area, Perimeter, and Volume Geometry Assessments Area, Perimeter, and Volume Introduction The performance tasks in this chapter focus on applying the properties of triangles and polygons to

More information

Su.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)

Su.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular) MA.912.G.2 Geometry: Standard 2: Polygons - Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures

More information

COURSE OVERVIEW. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved

COURSE OVERVIEW. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved COURSE OVERVIEW The geometry course is centered on the beliefs that The ability to construct a valid argument is the basis of logical communication, in both mathematics and the real-world. There is a need

More information

MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume.

MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume. MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume For prisms, pyramids, cylinders, and cones: Volume is the area of one base

More information

Geometry. 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. 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 information

GEOMETRY FINAL EXAM REVIEW

GEOMETRY 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 information

INDEX. Arc Addition Postulate,

INDEX. Arc Addition Postulate, # 30-60 right triangle, 441-442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent

More information

Geometry FSA Mathematics Practice Test Questions

Geometry FSA Mathematics Practice Test Questions Geometry FSA Mathematics Practice Test Questions The purpose of these practice test materials is to orient teachers and students to the types of questions on paper-based FSA tests. By using these materials,

More information

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.

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. 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

2) 4.6 mi to ft A) 24,288 ft B) ft C)2024 ft D) 8096 ft. 3) 78 ft to yd A) 234 yd B) 2808 yd C)26 yd D) 8.67 yd

2) 4.6 mi to ft A) 24,288 ft B) ft C)2024 ft D) 8096 ft. 3) 78 ft to yd A) 234 yd B) 2808 yd C)26 yd D) 8.67 yd Review questions - test 2 MULTIPLE CHOICE. Circle the letter corresponding to the correct answer. Partial credit may be earned if correct work is shown. Use dimensional analysis to convert the quantity

More information

Assessment For The California Mathematics Standards Grade 3

Assessment For The California Mathematics Standards Grade 3 Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

More information

Geo - CH9 Practice Test

Geo - CH9 Practice Test Geo - H9 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the area of the parallelogram. a. 35 in 2 c. 21 in 2 b. 14 in 2 d. 28 in 2 2.

More information

Introduction. Rectangular Volume. Module #5: Geometry-Volume Bus 130 1:15

Introduction. Rectangular Volume. Module #5: Geometry-Volume Bus 130 1:15 Module #5: Geometry-olume Bus 0 :5 Introduction In this module, we are going to review the formulas for calculating volumes, rectangular, cylindrical, and irregular shaped. To set the stage, let s suppose

More information