11-5 Polygons ANSWER: ANSWER: ANSWER:

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "11-5 Polygons ANSWER: ANSWER: ANSWER:"

Transcription

1 Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why KALEIDOSCOPE The kaleidoscope image shown is a regular polygon with 14 sides. What is the measure of one interior angle of the polygon? Round to the nearest tenth. The figure is not a polygon because it is an open figure. Two of the sides are not connected The figure has 8 sides that only intersect at their endpoints. It is an octagon. 6. Determine whether or not an equilateral triangle can be used to make a tessellation. If not, explain. yes 3. Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. 7. The figure has 5 sides that only intersect at their endpoints. It is a pentagon. 4. MULTIPLE CHOICE The sum of the measures of the interior angles of a certain regular polygon is How many sides does this polygon have? A 9 sides B 10 sides C 11 sides D 12 sides D 8. The figure has 5 sides that only intersect at their endpoints. It is a pentagon. The figure has 8 sides that only intersect at their endpoints. It is an octagon. esolutions Manual - Powered by Cognero Page 1

2 The figure has 6 sides that only intersect at their endpoints. It is a hexagon. The figure is not a polygon because it has sides that cross each other. The figure has 9 sides that only intersect at their endpoints. It is a nonagon gon gon NATURE The individual cells of a honeycomb are hexagons. What is the measure of an interior angle of a honeycomb? ARCHITECTURE The dome in a state capitol building is octagonal. What is the measure of an interior angle of an octagon? 135 Determine whether or not a tessellation can be created using each regular polygon. If not, explain. 19. quadrilateral yes gon The figure is not a polygon because it has a curved side. Find the sum of the measures of the interior angles of each polygon. 13. decagon gon 1620 no; Each interior angle of a regular 12-gon measures 150 and 360 is not evenly divisible by gon no; Each interior angle of a regular 15-gon measures 156 and 360 is not evenly divisible by gon no; Each interior angle of a regular 20-gon measures 162 and 360 is not evenly divisible by 162. esolutions Manual - Powered by Cognero Page 2

3 Identify the polygon given the sum of the interior angle measures º octagon º 15-gon º 20-gon º 30-gon TESSELLATIONS You can create a tessellation using a translation. a. Draw a square. Then draw a triangle inside the top of the square. b. Translate or slide the triangle from the top to the bottom of the square. c. Repeat this pattern unit to create a tessellation. Use a translation to create a tessellation for each pattern shown ART Refer to the mosaic below. 29. How are tessellations used to create the image? The artist used translations of a square and an octagon to make the tessellating pattern. esolutions Manual - Powered by Cognero Page 3

4 OPEN ENDED Use two types of polygons to create a tessellation that is different from the tessellations shown in this lesson. Describe the polygons and the transformation that you used. Sample answer: When a side of a polygon is extended, an exterior angle is formed. In any polygon, the sum of the measures of the exterior angles, one at each vertex, is 360. Find the measure of an exterior angle of each regular polygon. 31. triangle octagon 45 squares, equilateral triangles; translations, reflections, or rotations 36. REASONING If the number of sides of a regular polygon increases by 1, what happens to the sum of the measures of the interior angles? It increases by ERROR ANALYSIS Jacinta says that it is possible to use a trapezoid to create a tessellation. Robert says this is impossible because the interior angles of a trapezoid are not congruent. Is either of them correct? Explain your reasoning. Jacinta; the interior angles of a polygon do not have to be congruent in order to create a tessellation. The sum of their measures at a vertex must equal decagon gon 24 esolutions Manual - Powered by Cognero Page 4

5 38. CHALLENGE Create a tessellation using regular hexagons and equilateral triangles. 39. WRITING IN MATH Describe the difference between a regular polygon and a polygon that is irregular. Then explain the process used to find the interior angle measure of a regular polygon. Sample answer: A regular polygon has all sides congruent and all angles congruent. A polygon that is not regular has different side lengths, different angle measures, or both. To find the interior angle measure of a regular polygon, subtract 2 from the number of sides, multiply the result by 180, then divide that result by the number of angles. 40. Which term identifies the shaded part of the design shown? 41. The sum of the measures of the interior angles of a polygon is Find the number of sides of the polygon. F 10 G 14 H 16 J 18 G 42. A landscape architect is looking for a brick paver shape that will tessellate. Which shape by itself will allow her to tessellate a patio area? A B C D A heptagon B hexagon C octagon D pentagon B A 43. GRIDDED RESPONSE What is the measure in degrees of an interior angle of a regular polygon with 20 sides? 162 Determine whether each statement is sometimes, always or never true. 44. A square is a rhombus. always esolutions Manual - Powered by Cognero Page 5

6 45. A parallelogram is a rectangle. sometimes 46. A rectangle is a square. sometimes 47. A parallelogram is a quadrilateral. always 48. A figure has vertices A( 3, 2), B( 1, 1), C( 2, 3), and D( 4, 2). Graph the figure and its image after a rotation of 180 around the origin. 50. GARDENING Suppose you plant a square garden with an area of 300 square feet. What is the minimum amount of fencing needed to enclose the garden if the fencing only comes in whole-foot sections? 70 ft of fencing 51. ALGEBRA Solve x Graph the solution on a number line. x 9.6 Find each quotient ( 8) ( 12) 49. Determine whether the triangles shown are congruent. If so, name the corresponding parts and write a congruence statement Simplify each expression. 56. (5 2) yes; M O, L PNO, LNM P, 57. (7 2) esolutions Manual - Powered by Cognero Page 6

7 58. (10 2) (9 2) esolutions Manual - Powered by Cognero Page 7

1 of 69 Boardworks Ltd 2004

1 of 69 Boardworks Ltd 2004 1 of 69 2 of 69 Intersecting lines 3 of 69 Vertically opposite angles When two lines intersect, two pairs of vertically opposite angles are formed. a d b c a = c and b = d Vertically opposite angles are

More information

7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014

7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014 Chapter 7 Polygons Polygon 1. Closed Figure # of Sides Polygon Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 2. Straight sides/edges 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon 15 Pentadecagon

More information

UNIT H1 Angles and Symmetry Activities

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)

More information

11.3 Curves, Polygons and Symmetry

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

More information

Geometry. Unit 6. Quadrilaterals. Unit 6

Geometry. Unit 6. Quadrilaterals. Unit 6 Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections

More information

6-1 Properties and Attributes of Polygons

6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. A? is a three-sided polygon. triangle 2. A? is a four-sided polygon. quadrilateral Evaluate each expression

More information

Target To know the properties of a rectangle

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

More information

POLYGONS

POLYGONS POLYGONS 8.1.1 8.1.5 After studying triangles and quadrilaterals, students now extend their study to all polygons. A polygon is a closed, two-dimensional figure made of three or more nonintersecting straight

More information

11-6 Area: Parallelograms, Triangles, and Trapezoids

11-6 Area: Parallelograms, Triangles, and Trapezoids 1. 6. LACROSSE A lacrosse goal with net is shown. The goal is 6 feet wide, 6 feet high, and 7 feet deep. What is the area of the triangular region of the ground inside the net? 30.5 ft 2 2. 21 ft 2 14.08

More information

Polygons are figures created from segments that do not intersect at any points other than their endpoints.

Polygons are figures created from segments that do not intersect at any points other than their endpoints. Unit #5 Lesson #1: Polygons and Their Angles. Polygons are figures created from segments that do not intersect at any points other than their endpoints. A polygon is convex if all of the interior angles

More information

6-1 Angles of Polygons

6-1 Angles of Polygons Find the sum of the measures of the interior angles of each convex polygon. 1. decagon A decagon has ten sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.

More information

Unit 8. Ch. 8. "More than three Sides"

Unit 8. Ch. 8. More than three Sides Unit 8. Ch. 8. "More than three Sides" 1. Use a straightedge to draw CONVEX polygons with 4, 5, 6 and 7 sides. 2. In each draw all of the diagonals from ONLY ONE VERTEX. A diagonal is a segment that joins

More information

November 11, Polygons. poly means "many" gon means "angles" polygon means "many angles"

November 11, Polygons. poly means many gon means angles polygon means many angles 3.5 Polygons poly means "many" gon means "angles" polygon means "many angles" note that each polygon is formed by coplanar segments (called sides) such that: each segment intersects exactly 2 other segments,

More information

Geometry. 1.4 Perimeter and Area in the Coordinate Plane

Geometry. 1.4 Perimeter and Area in the Coordinate Plane Geometry 1.4 Perimeter and Area in the Coordinate Plane Essential Question How can I find the perimeter and area of a polygon in a coordinate plane? What You Will Learn Classify polygons Find perimeters

More information

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? 1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional

More information

TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements.

TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements. TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements. The student will select an appropriate representation to solve

More information

The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons.

The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. Interior Angles of Polygons The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. The sum of the measures of the interior angles of a triangle

More information

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon. hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.

More information

Perimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this.

Perimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this. UNIT 10 Perimeter and Area An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this. 3 UNIT 10 PERIMETER AND AREA You can find geometric shapes in

More information

15 Polygons. 15.1 Angle Facts. Example 1. Solution. Example 2. Solution

15 Polygons. 15.1 Angle Facts. Example 1. Solution. Example 2. Solution 15 Polygons MEP Y8 Practice Book B 15.1 Angle Facts In this section we revise some asic work with angles, and egin y using the three rules listed elow: The angles at a point add up to 360, e.g. a c a +

More information

Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period

Unit 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 information

10.1: Areas of Parallelograms and Triangles

10.1: Areas of Parallelograms and Triangles 10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a

More information

The Polygon Angle-Sum Theorems

The Polygon Angle-Sum Theorems 6-1 The Polygon Angle-Sum Theorems Common Core State Standards G-SRT.B.5 Use congruence... criteria to solve problems and prove relationships in geometric figures. MP 1, MP 3 Objectives To find the sum

More information

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3 Geometry Concepts Figures that lie in a plane are called plane figures. These are all plane figures. Polygon No. of Sides Drawing Triangle 3 A polygon is a plane closed figure determined by three or more

More information

Study Guide. 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. Note: Figure is not drawn to scale.

Study Guide. 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. Note: Figure is not drawn to scale. Study Guide Name Test date 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. 1. Note: Figure is not drawn to scale. If x = 14 units and h = 6 units, then what is the area of the triangle

More information

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 1-7 HW: Pgs: 8-10 DAY 2: (6-2) Pgs:

More information

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 AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

More information

A of a polygon is a segment that joins two nonconsecutive vertices. 1. How many degrees are in a triangle?

A of a polygon is a segment that joins two nonconsecutive vertices. 1. How many degrees are in a triangle? 8.1- Find Angle Measures in Polygons SWBAT: find interior and exterior angle measures in polygons. Common Core: G.CO.11, G.CO.13, G.SRT.5 Do Now Fill in the blank. A of a polygon is a segment that joins

More information

Sum of the interior angles of a n-sided Polygon = (n-2) 180

Sum of the interior angles of a n-sided Polygon = (n-2) 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 n-sided Polygon = (n-2) 180 What you need to know: How to use the formula

More information

Unit 3: Triangle Bisectors and Quadrilaterals

Unit 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 information

parallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect

parallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect parallel lines lines that stay same distance from each other forever and never intersect perpendicular lines lines that cross at a point and form 90 angles intersecting lines vertices lines that cross

More information

Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon.

Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon. ngles of Polygons Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon. Vocabulary diagonal does a scallop shell illustrate

More information

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures Math 6: Unit 7: Geometry Notes -Dimensional Figures Prep for 6.G.A.1 Classifying Polygons A polygon is defined as a closed geometric figure formed by connecting line segments endpoint to endpoint. Polygons

More information

Geometry Chapter 9 Extending Perimeter, Circumference, and Area

Geometry Chapter 9 Extending Perimeter, Circumference, and Area Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Target (LT-1) Solve problems involving the perimeter and area of triangles

More information

11-4 Areas of Regular Polygons and Composite Figures

11-4 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 information

Polygon Properties and Tiling

Polygon Properties and Tiling ! Polygon Properties and Tiling You learned about angles and angle measure in Investigations and 2. What you learned can help you figure out some useful properties of the angles of a polygon. Let s start

More information

Geometry Chapter 9 Extending Perimeter, Circumference, and Area

Geometry Chapter 9 Extending Perimeter, Circumference, and Area Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Targets LT9-1: Solve problems involving the perimeter and area of

More information

A regular polygon with three sides is an equilateral triangle. A regular polygon with four sides is a square.

A regular polygon with three sides is an equilateral triangle. A regular polygon with four sides is a square. What is a tiling? A tiling refers to any pattern that covers a flat surface, like a painting on a canvas, using non-overlapping repetitions. Another word for a tiling is a tessellation. There are several

More information

A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft. F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 5 in

A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft. F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 5 in 7.5 The student will a) describe volume and surface area of cylinders; b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and c) describe how changing

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

Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website

Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 5-50 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1 NCTM Standards Addressed Problem Solving Geometry Algebra

More information

Line. A straight path that continues forever in both directions.

Line. A straight path that continues forever in both directions. Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A

More information

SHOW YOUR WORK CHECK YOUR WORK VALIDATE YOUR WORK! Unit 6: POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT???

SHOW YOUR WORK CHECK YOUR WORK VALIDATE YOUR WORK! Unit 6: POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT??? Unit 6: POLYGONS Are these polygons? Justify your answer by explaining WHY or WHY NOT??? a) b) c) Yes or No Why/Why not? Yes or No Why/Why not? Yes or No Why/Why not? a) What is a CONCAVE polygon? Use

More information

Lesson 6: Polygons and Angles

Lesson 6: Polygons and Angles Lesson 6: Polygons and Angles Selected Content Standards Benchmark Assessed: G.4 Using inductive reasoning to predict, discover, and apply geometric properties and relationships (e.g., patty paper constructions,

More information

11-2 Areas of Trapezoids, Rhombi, and Kites. Find the area of each trapezoid, rhombus, or kite. 1. SOLUTION: 2. SOLUTION: 3.

11-2 Areas of Trapezoids, Rhombi, and Kites. Find the area of each trapezoid, rhombus, or kite. 1. SOLUTION: 2. SOLUTION: 3. Find the area of each trapezoid, rhombus, or kite. 1. 2. 3. esolutions Manual - Powered by Cognero Page 1 4. OPEN ENDED Suki is doing fashion design at 4-H Club. Her first project is to make a simple A-line

More information

MATH 139 FINAL EXAM REVIEW PROBLEMS

MATH 139 FINAL EXAM REVIEW PROBLEMS MTH 139 FINL EXM REVIEW PROLEMS ring a protractor, compass and ruler. Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice

More information

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386

More information

Topic : Exterior Angles - Worksheet How many degrees are there in the sum of the exterior angles of a regular hexagon?

Topic : Exterior Angles - Worksheet How many degrees are there in the sum of the exterior angles of a regular hexagon? Topic : Exterior Angles - Worksheet 1 regular hexagon? polygon having 20 3. If each polygon contains 40 O how many each polygon having 16 angle of a regular polygon having 8 a 5 sided polygon? polygon

More information

Grade 3 Core Standard III Assessment

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

More information

Unit 8 Geometry QUADRILATERALS. NAME Period

Unit 8 Geometry QUADRILATERALS. NAME Period Unit 8 Geometry QUADRILATERALS NAME Period 1 A little background Polygon is the generic term for a closed figure with any number of sides. Depending on the number, the first part of the word Poly is replaced

More information

State whether the figure appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number.

State whether the figure appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number. State whether the figure appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number. esolutions Manual - Powered by Cognero Page 1 1. A figure

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

Geometry Progress Ladder

Geometry Progress Ladder Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

More 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

Tessellations. A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps.

Tessellations. A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps. Tessellations Katherine Sheu A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps. 1. The picture below can be extended to a tessellation

More information

Third Grade Illustrated Math Dictionary Updated 9-13-10 As presented by the Math Committee of the Northwest Montana Educational Cooperative

Third Grade Illustrated Math Dictionary Updated 9-13-10 As presented by the Math Committee of the Northwest Montana Educational Cooperative Acute An angle less than 90 degrees An acute angle is between 1 and 89 degrees Analog Clock Clock with a face and hands This clock shows ten after ten Angle A figure formed by two line segments that end

More information

Tessellations and Tile Patterns

Tessellations and Tile Patterns Tessellations and Tile Patterns Definitions: Tessellation covering, or tiling, of a plane with a pattern of figures so there are no overlaps or gaps. Monohedral tiling tessellation made up of congruent

More information

Lesson 1: Exploring Polygons

Lesson 1: Exploring Polygons Lesson 1: Exploring Polygons Objectives: Students will be able to identify whether a given shape is a polygon using the properties of polygons. Students will be able to identify and name polygons that

More information

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane.

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. Symmetry When you can fold a figure in half, with both sides congruent, the fold line

More information

A. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.

A. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. Geometry - Areas of Parallelograms A. Areas of Parallelograms. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. A B Ex: See how VDFA V CGB so rectangle

More information

Fifth Grade. Scope & Sequence of Lessons. by lesson number

Fifth Grade. Scope & Sequence of Lessons. by lesson number Scope & Sequence of Lessons by lesson number PLACE VALUE AND COUNTING Place value 1 Recognizing numbers less than a million 65 Recognizing tenths and hundredths places 80 Recognizing numbers up through

More information

4 th Grade MCA3 Standards, Benchmarks, Test Specifications & Sampler Questions

4 th Grade MCA3 Standards, Benchmarks, Test Specifications & Sampler Questions Number & Operation 18 22 Items 4 th Grade MCA3 Standards, Benchmarks, Test Specifications & Sampler Questions Standard No. Benchmark (4 th Grade) Sampler Item Demonstrate mastery of Demonstrate fluency

More information

Mensuration Introduction

Mensuration Introduction Mensuration Introduction Mensuration is the process of measuring and calculating with measurements. Mensuration deals with the determination of length, area, or volume Measurement Types The basic measurement

More information

Area. Area Overview. Define: Area:

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.

More information

Tons of Free Math Worksheets at:

Tons of Free Math Worksheets at: Topic: Sum of Interior Angles- Worksheet 1 a pentagon? nine 3. If the polygon equals 1080, then determine the 1620º? interior angles equals 6840s? n eighteen a Octagon? seventeen polygon equals 1980, how

More information

8-2 Classifying Angles Objective: Identify different types of angles Explain how to determine the type of angle.

8-2 Classifying Angles Objective: Identify different types of angles Explain how to determine the type of angle. 8-1 Classifying Lines Objective: Identify type of lines and line relationships Language Objective: Classify and then justify your classification Vocabulary: line- continues in both directions for ever

More information

Math Dictionary Terms for Grades K-1:

Math Dictionary Terms for Grades K-1: Math Dictionary Terms for Grades K-1: A Addend - one of the numbers being added in an addition problem Addition - combining quantities And - 1) combine, 2) shared attributes, 3) represents decimal point

More information

An arrangement that shows objects in rows and columns Example:

An arrangement that shows objects in rows and columns Example: 1. acute angle : An angle that measures less than a right angle (90 ). 2. addend : Any of the numbers that are added 2 + 3 = 5 The addends are 2 and 3. 3. angle : A figure formed by two rays that meet

More information

Pre-Algebra IA Grade Level 8

Pre-Algebra IA Grade Level 8 Pre-Algebra IA Pre-Algebra IA introduces students to the following concepts and functions: number notation decimals operational symbols inverse operations of multiplication and division rules for solving

More information

13-3 Geometric Probability. 1. P(X is on ) SOLUTION: 2. P(X is on ) SOLUTION:

13-3 Geometric Probability. 1. P(X is on ) SOLUTION: 2. P(X is on ) SOLUTION: Point X is chosen at random on. Find the probability of each event. 1. P(X is on ) 2. P(X is on ) 3. CARDS In a game of cards, 43 cards are used, including one joker. Four players are each dealt 10 cards

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

Page How many sides does an octagon have? a) 4 b) 5 c) 6 d) 8 e) A regular hexagon has lines of symmetry. a) 2 b) 3 c) 4 d) 5 e) 6 1 9

Page How many sides does an octagon have? a) 4 b) 5 c) 6 d) 8 e) A regular hexagon has lines of symmetry. a) 2 b) 3 c) 4 d) 5 e) 6 1 9 Acc. Geometery Name Polygon Review Per/Sec. Date Determine whether each of the following statements is always, sometimes, or never true. 1. A regular polygon is convex. 2. Two sides of a polygon are noncollinear.

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

Grade 4 Math Expressions Vocabulary Words

Grade 4 Math Expressions Vocabulary Words Grade 4 Math Expressions Vocabulary Words Link to Math Expression Online Glossary for some definitions: http://wwwk6.thinkcentral.com/content/hsp/math/hspmathmx/na/gr4/se_9780547153131_/eglos sary/eg_popup.html?grade=4

More information

1-6 Two-Dimensional Figures. Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

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

More information

Upper Elementary Geometry

Upper Elementary Geometry Upper Elementary Geometry Geometry Task Cards Answer Key The unlicensed photocopying, reproduction, display, or projection of the material, contained or accompanying this publication, is expressly prohibited

More information

Activity Set 4. Trainer Guide

Activity Set 4. Trainer Guide Geometry and Measurement of Plane Figures Activity Set 4 Trainer Guide Int_PGe_04_TG GEOMETRY AND MEASUREMENT OF PLANE FIGURES Activity Set #4 NGSSS 3.G.3.1 NGSSS 3.G.3.3 NGSSS 4.G.5.1 NGSSS 5.G.3.1 Amazing

More information

Chapter 3. Chapter 3 Opener. Section 3.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 101) So, the value of x is 112.

Chapter 3. Chapter 3 Opener. Section 3.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 101) So, the value of x is 112. Chapter 3 Opener Try It Yourself (p. 101) 1. The angles are vertical. x + 8 120 x 112 o, the value of x is 112. 2. The angles are adjacent. ( x ) + 3 + 43 90 x + 46 90 x 44 o, the value of x is 44. 3.

More information

19. [Shapes] less than. The angle appears greater than 90. Check by placing the corner of a Maths Mate page inside the angle.

19. [Shapes] less than. The angle appears greater than 90. Check by placing the corner of a Maths Mate page inside the angle. 19. [Shapes] Skill 19.1 Comparing angles to a right angle. Place the corner of a page (which is a right angle) at the corner (vertex) of the angle. Align the base of the page with one line of the angle.

More information

Remaining Fractions Two-Step Equations

Remaining Fractions Two-Step Equations Remaining Fractions Two-Step Equations Lesson 61 61 Remaining Fractions If a whole has been divided into parts and we know the size of one part, then we can figure out the size of the other parts. What

More information

Shape Dictionary YR to Y6

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

More information

Sum of the interior angles of a (n - 2)180 polygon ~, Sum of the exterior angles of a 360 polygon

Sum of the interior angles of a (n - 2)180 polygon ~, Sum of the exterior angles of a 360 polygon Name Geometry Polygons Sum of the interior angles of a (n - 2)180 polygon ~, Sum of the exterior angles of a 360 polygon Each interior angle of a regular (n - 2)180 i polygon n Each exterior angle of a

More information

Grade 3 Math Expressions Vocabulary Words

Grade 3 Math Expressions Vocabulary Words Grade 3 Math Expressions Vocabulary Words Unit 1, Book 1 Place Value and Multi-Digit Addition and Subtraction OSPI words not used in this unit: add, addition, number, more than, subtract, subtraction,

More information

acute angle acute triangle Cartesian coordinate system concave polygon congruent figures

acute angle acute triangle Cartesian coordinate system concave polygon congruent figures acute angle acute triangle Cartesian coordinate system concave polygon congruent figures convex polygon coordinate grid coordinates dilatation equilateral triangle horizontal axis intersecting lines isosceles

More information

Rounding Decimal Numbers

Rounding Decimal Numbers Rounding Decimal Numbers Reteaching Math Course, Lesson To round decimal numbers: Circle the place value you are rounding to. Underline the digit to its right. If the underlined number is or more, add

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

CLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS - SIMPLE CLOSED CURVE FIGURES AND POLYGONS

CLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS - SIMPLE CLOSED CURVE FIGURES AND POLYGONS CLASSIFIED NOMENCLATURE: THE FORMATION OF REGIONS - SIMPLE CLOSED CURVE FIGURES AND POLYGONS Material: Geometry Stick Box and Board A piece of string Paper and scissors Paper labels and pencil Presentation:

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

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 - Chapter 1. Use the figure to name each of the following.

Practice Test - Chapter 1. Use the figure to name each of the following. Use the figure to name each of the following. 1. the line that contains points Q and Z The points Q and Z lie on the line b, line b 2. two points that are coplanar with points W, X, and Y Coplanar points

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

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

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

Shapes & Designs Notes

Shapes & Designs Notes Problem 1.1 Definitions: regular polygons - polygons in which all the side lengths and angles have the same measure edge - also referred to as the side of a figure tiling - covering a flat surface with

More information

Estimating Angle Measures

Estimating 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 information

The Elementary School Math Project. Mirror, Mirror

The Elementary School Math Project. Mirror, Mirror The Elementary School Math Project Mirror, Mirror Math Grows Up (Geometry/Spatial Sense) Objective Students will use spatial reasoning and problem solving strategies to determine which regular polygons

More information

Perimeter and area formulas for common geometric figures:

Perimeter 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 information

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the

More information

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 of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams: Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of

More information

Grade 6 Math Circles Winter February 24/25. Angle

Grade 6 Math Circles Winter February 24/25. Angle Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles Winter 2015 - February 24/25 Angles Introduction At this point in your mathematical

More information