CHAPTER 3 Chapter Opener (slide 2) Getting Ready (slides 3 to 9) Mid-Chapter FAQ (slides 10 and 11) Chapter FAQ (slides 12 to 15) Chapter 3 Task (slides 16 to 18) Lessons 3.1 – 3.3 (separate files) Lessons 3.4 – 3.6 (separate files) Tech Tip This graphic organizer allows you to navigate to slides corresponding to the start, middle, and end of the chapter. You can return to this file as needed. Individual lessons are located in separate files. Print or copy any attachments you think you will need in class.

Once you have classified a shape, you know a lot about it. What shapes do you recognize here? What do you know about each shape? Plane Geometry 3

B Answer 1Which equation matches this diagram? A 180° – 60° = x B x + 60° = 90° C 360° – 60° = x D x + 60° = 180° Getting Ready 60° x 3 Plane Geometry

A Answer 2Which equation matches this diagram? A 70° + 25° + y = 180° B 360° – 70° – 25° = y C 25° + y = 70° D 70° + 25° = y 25° y 70° Getting Ready 3 Plane Geometry

B Answer 3What is the value of d ? A 5° B 85° C 90° D 105° 85° d Getting Ready 3 Plane Geometry

C Answer 4What is the sum of the measures of the angles of a triangle? A 60° B 90° C 180° D 360° Getting Ready 3 Plane Geometry

C Answer 5What is the value of x ? A 55° B 95° C 125° D 145° 125° x Getting Ready 3 Plane Geometry

False Answer 6Parallel lines intersect. True False Getting Ready 3 Plane Geometry

D Answer 7Which shape is a quadrilateral? A B C D Getting Ready 3 Plane Geometry

Method 1: Remember that supplementary angles sum to 180°. Find those angles that make up a straight line. Look at line EC. ∠ EBA and ∠ ABC form a straight line. They will sum to 180° so ∠ ABC = 180° – 35° = 145°. ∠ CBD and ∠ ABC form a straight line, so ∠ CBD = 180° – ∠ ABC ∠ CBD = 180° – 145° = 35°. So ∠ DBE measures 135° because it forms a straight line when combined with ∠ CBD. 35° B E A C D Mid-Chapter FAQ How do I find the missing angles if I am given intersecting lines? Q A Reveal 3 Plane Geometry

Method 2: Remember that angles that are opposite to each other are equal. ∠ CBD is opposite ∠ EBA. This means that ∠ EBA = 35° because the angles must be equal. ∠ EBA and ∠ ABC form a straight line. They will sum to 180° so ∠ ABC = 180° – 35° = 145°. ∠ ABC is opposite ∠ EBD so they must be equal. ∠ EBD is 145°. 35° B E A C D How do I find the missing angles if I am given intersecting lines? Mid-Chapter FAQ Q A Reveal 3 Plane Geometry

Method 2: ∠ FGH and ∠ GKM are corresponding angles, so they are equal. ∠ GKM = 30° ∠ GKM and ∠ GKJ form a straight line. They sum to 180°. ∠ GKJ = 180° – 30° = 150° Reveal 30° L M F J I H K G x Given two parallel lines and a transversal, how can I determine an unknown angle? Method 1: ∠ IGK is opposite ∠ FGH, so they are equal. ∠ IGK = 30° ∠ IGK and ∠ GKJ are interior angles on the same side of the transversal, so they sum to 180°. ∠ GKJ = 180° – 30° = 150° A1 A2 Chapter FAQ Q 3 Plane Geometry Reveal

3 Plane Geometry If I have been given two of the interior angles of a triangle, how do I find the exterior angle of the triangle? Method 1: The interior angles of a triangle sum to 180°. ∠ CBD = 180° – 27° – 65° = 88°. ∠ CBD and ∠ ABC form a straight line, so sum to 180°. ∠ ABC = 180°– ∠ CBD = 180° – 88° = 92° Method 2: The sum of the two given angles equals the exterior angle required. ∠ BCD + ∠ CDB = 27° + 65° = 92°, so ∠ ABC = 92° 27° B A C D x 65° Chapter FAQ A1 A2 Q Reveal

27° B A C D 65° How do I find the missing angles of the quadrilateral? Since AB and DC are parallel, the sum of ∠ C and ∠ B is 180°. ∠ C = 180° – 27° = 153°. The sum of the interior angles of a quadrilateral is 360°. Since I know three angles, I can subtract them from 360° to find ∠ D. ∠ D = 360° – 65° – 27° – 153° = 115° Chapter FAQ A Q Reveal 3 Plane Geometry

The sum of the interior angles of a polygon can be expressed as 180°(n – 2). For a hexagon, 180°[(6) – 2] = 720° Since the polygon is regular, all angles are equal. A hexagon has 6 sides, so divide 720° by 6 to get 120°. If I am given a regular polygon, what would one of the interior angles measure? Chapter FAQ A Q Reveal 3 Plane Geometry

Chapter 3 Task Designing a Park A town council has decided to build a local park. The park should be a fun place for people to visit, but also have a formal feel. Create a design for the park. 3 Plane Geometry

DESIGN CRITERIA Include parallel lines, transversals, and polygons in your design. Include angle measures, but only one angle should have been measured using a protractor. Chapter 3 Task Designing a Park 3 Plane Geometry

REPORT CRITERIA Include a drawing of your design. Describe the features of the park and their benefits. Describe the angle relationships and other properties you used to determine the angle measures. Chapter 3 Task Designing a Park 3 Plane Geometry