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Geometry 5.2 Inside Out.

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Presentation on theme: "Geometry 5.2 Inside Out."β€” Presentation transcript:

1 Geometry 5.2 Inside Out

2 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

3 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)

4 π‘₯=180βˆ’128 π‘₯= 52 π‘œ Linear Pair Postulate 52+75+𝑦=180 𝑦+127=180 𝑦= 53 π‘œ

5 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? β€œThe sum of the measures of the interior angles of a triangle is 180 π‘œ .”

6 π‘‡π‘Ÿπ‘–π‘Žπ‘›π‘”π‘™π‘’ 𝐴𝐡𝐢 π‘€π‘–π‘‘β„Ž 𝐴𝐡 βˆ₯ 𝐢𝐷
π‘šβˆ 4+π‘šβˆ 3+π‘šβˆ 5= 180 π‘œ ∠1β‰…βˆ 4, ∠2β‰…βˆ 5 π‘šβˆ 1=π‘šβˆ 4, π‘šβˆ 2=π‘šβˆ 5 π‘šβˆ 1+π‘šβˆ 3+π‘šβˆ 2= 180 π‘œ π‘šβˆ 1+π‘šβˆ 2+π‘šβˆ 3= 180 π‘œ 𝐺𝑖𝑣𝑒𝑛 𝐴𝑛𝑔𝑙𝑒 π΄π‘‘π‘‘π‘–π‘‘π‘–π‘œπ‘› π‘ƒπ‘œπ‘ π‘‘π‘’π‘™π‘Žπ‘‘π‘’ π΄π‘™π‘‘π‘’π‘Ÿπ‘›π‘Žπ‘‘π‘’ πΌπ‘›π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿ 𝐴𝑛𝑔𝑙𝑒 π‘‡β„Žπ‘š π·π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘œπ‘“ πΆπ‘œπ‘›π‘”π‘Ÿπ‘’π‘’π‘›π‘‘ 𝐴𝑛𝑔𝑙𝑒𝑠 π‘†π‘’π‘π‘ π‘‘π‘–π‘‘π‘’π‘‘π‘–π‘œπ‘› π‘ƒπ‘Ÿπ‘œπ‘π‘’π‘Ÿπ‘‘π‘¦ π΄π‘ π‘ π‘œπ‘π‘–π‘Žπ‘‘π‘–π‘£π‘’ π‘ƒπ‘Ÿπ‘œπ‘π‘’π‘Ÿπ‘‘π‘¦

7 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)

8 Problem 2: Analyzing Triangles
Discuss #7 Together 47 π‘œ 98 π‘œ 95 π‘œ 112 π‘œ

9 Formative Assessment Skills Practice 5.2 Pg (1-12)

10 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

11 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

12 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. π‘šβˆ 4=π‘šβˆ 1+π‘šβˆ 2

13 Sketchpad Example 5.2 Day 2 Exterior Angles

14 Problem 3: Exterior Angles
Discuss #14 Together

15 Problem 3: Exterior Angles
Discuss #14 Together

16 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 π‘šβˆ 4>π‘šβˆ 1 π‘Žπ‘›π‘‘ π‘šβˆ 4>π‘šβˆ 2

17 Talk the Talk Pg. 403 Collaborate 2 Minutes
Shortest to Longest b, a, c, e, d c a d π‘ˆπ‘ π‘–π‘›π‘” π‘‘β„Žπ‘’ π‘‘π‘Ÿπ‘–π‘Žπ‘›π‘”π‘™π‘’ π‘œπ‘› π‘‘β„Žπ‘’ π‘Ÿπ‘–π‘”β„Žπ‘‘, π‘‘β„Žπ‘’ 𝑠𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘β„Žπ‘’ 32 π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝑖𝑠 π‘‘β„Žπ‘’ π‘ β„Žπ‘œπ‘Ÿπ‘‘π‘’π‘ π‘‘ 𝑠𝑖𝑑𝑒, π‘‚π‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘β„Žπ‘’ 58 π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝑖𝑠 𝑛𝑒π‘₯𝑑 π‘Žπ‘›π‘‘ π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘β„Žπ‘’ 90 π‘œ 𝑖𝑠 π‘‘β„Žπ‘’ π‘™π‘œπ‘›π‘”π‘’π‘ π‘‘ 𝑠𝑖𝑑𝑒 πΉπ‘’π‘Ÿπ‘‘β„Žπ‘’π‘Ÿπ‘šπ‘œπ‘Ÿπ‘’, π‘€β„Žπ‘’π‘› 𝑒𝑠𝑖𝑛𝑔 π‘‘β„Žπ‘’ π‘‘π‘Ÿπ‘–π‘Žπ‘›π‘”π‘™π‘’ π‘œπ‘› π‘‘β„Žπ‘’ 𝑙𝑒𝑓𝑑, π‘‘β„Žπ‘’ 𝑠𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘β„Žπ‘’ 32 π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝑖𝑠 π‘‘β„Žπ‘’ π‘ β„Žπ‘œπ‘Ÿπ‘‘π‘’π‘ π‘‘ 𝑠𝑖𝑑𝑒 π‘‘β„Žπ‘’ 𝑠𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘β„Žπ‘’ 43 π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝑖𝑠 𝑛𝑒π‘₯𝑑 π‘Žπ‘›π‘‘ π‘‘β„Žπ‘’ 𝑠𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘β„Žπ‘’ 105 π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝑖𝑠 π‘‘β„Žπ‘’ π‘™π‘œπ‘›π‘”π‘’π‘ π‘‘ 𝑠𝑖𝑑𝑒 Lemon and Grape Islands are farthest apart

18 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.

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