Geometry 5.2 Inside Out

5.2 Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems Objectives Prove the triangle sum theorem Explore the relationship between the interior angle measures and the side lengths of a triangle Identify the remote interior angles of a triangle Identify the exterior angle of a triangle Explore the relationship between the exterior angle measures and two remote interior angles Prove the Exterior Angle Theorem Prove the Exterior Angle Inequality Theorem

Yes Can subtract from 180 to find the interior angles (linear pairs) Then all angles inside add to 180 Subtract from 180 to solve for x (linear pair)

𝑥=180−128 𝑥= 52 𝑜 Linear Pair Postulate 52+75+𝑦=180 𝑦+127=180 𝑦= 53 𝑜

Problem 1 Triangle Interior Angle Sums #1 Triangle Sum Theorem Draw a triangle on a sheet of paper Tear off the angles Place them next to each other What do you notice about the sum of these angles? “The sum of the measures of the interior angles of a triangle is 180 𝑜 .”

𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐴𝐵𝐶 𝑤𝑖𝑡ℎ 𝐴𝐵 ∥ 𝐶𝐷 𝑚∠4+𝑚∠3+𝑚∠5= 180 𝑜 ∠1≅∠4, ∠2≅∠5 𝑚∠1=𝑚∠4, 𝑚∠2=𝑚∠5 𝑚∠1+𝑚∠3+𝑚∠2= 180 𝑜 𝑚∠1+𝑚∠2+𝑚∠3= 180 𝑜 𝐺𝑖𝑣𝑒𝑛 𝐴𝑛𝑔𝑙𝑒 𝐴𝑑𝑑𝑖𝑡𝑖𝑜𝑛 𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑒 𝐼𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝐴𝑛𝑔𝑙𝑒 𝑇ℎ𝑚 𝐷𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝐶𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡 𝐴𝑛𝑔𝑙𝑒𝑠 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝐴𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑖𝑣𝑒 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦

Problem 2: Analyzing Triangles Collaborate 1, 2, or 3 (5 Minutes) Use Ruler and Protractor Each member of the group will do only one drawing Collaborate 4-6 (3 Minutes)

Problem 2: Analyzing Triangles Discuss #7 Together 47 𝑜 98 𝑜 95 𝑜 112 𝑜

Formative Assessment Skills Practice 5.2 Pg. 483-485 (1-12)

5.2 Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems Objectives Prove the triangle sum theorem Explore the relationship between the interior angle measures and the side lengths of a triangle Identify the remote interior angles of a triangle Identify the exterior angle of a triangle Explore the relationship between the exterior angle measures and two remote interior angles Prove the Exterior Angle Theorem Prove the Exterior Angle Inequality Theorem

Problem 3: Exterior Angles Collaborate 1-8 (4 Minutes) Remote Interior Angles of a Triangle The two angles that are non-adjacent to the specified exterior angle

Problem 3: Exterior Angles Collaborate 9-12 (4 Minutes) Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle. 𝑚∠4=𝑚∠1+𝑚∠2

Sketchpad Example 5.2 Day 2 Exterior Angles

Problem 3: Exterior Angles Discuss #14 Together

Problem 3: Exterior Angles Discuss #14 Together

Problem 3: Exterior Angles Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of the remote interior angles of a triangle 𝑚∠4>𝑚∠1 𝑎𝑛𝑑 𝑚∠4>𝑚∠2

Talk the Talk Pg. 403 Collaborate 2 Minutes Shortest to Longest b, a, c, e, d c a d 𝑈𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡, 𝑡ℎ𝑒 𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 32 𝑜 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑡ℎ𝑒 𝑠ℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝑠𝑖𝑑𝑒, 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 58 𝑜 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑛𝑒𝑥𝑡 𝑎𝑛𝑑 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 90 𝑜 𝑖𝑠 𝑡ℎ𝑒 𝑙𝑜𝑛𝑔𝑒𝑠𝑡 𝑠𝑖𝑑𝑒 𝐹𝑢𝑟𝑡ℎ𝑒𝑟𝑚𝑜𝑟𝑒, 𝑤ℎ𝑒𝑛 𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡, 𝑡ℎ𝑒 𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 32 𝑜 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑡ℎ𝑒 𝑠ℎ𝑜𝑟𝑡𝑒𝑠𝑡 𝑠𝑖𝑑𝑒 𝑡ℎ𝑒 𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 43 𝑜 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑛𝑒𝑥𝑡 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 105 𝑜 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑡ℎ𝑒 𝑙𝑜𝑛𝑔𝑒𝑠𝑡 𝑠𝑖𝑑𝑒 Lemon and Grape Islands are farthest apart

Formative Assessment Skills Practice 5.2 Pg. 483 Vocabulary (1-4) Turn in all of 5.2 on the round table when finished. Both assignments are due today.