Download 5.2 Triangle Sum and Angle Comparison

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
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 = 52𝑜
Linear Pair Postulate
52 + 75 + 𝑦 = 180
𝑦 + 127 = 180
𝑦 = 53𝑜
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 180𝑜 .”
1.
2.
3.
4.
5.
6.
𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐴𝐵𝐶 𝑤𝑖𝑡ℎ 𝐴𝐵 ∥ 𝐶𝐷
𝑚∠4 + 𝑚∠3 + 𝑚∠5 = 180𝑜
∠1 ≅ ∠4, ∠2 ≅ ∠5
𝑚∠1 = 𝑚∠4, 𝑚∠2 = 𝑚∠5
𝑚∠1 + 𝑚∠3 + 𝑚∠2 = 180𝑜
𝑚∠1 + 𝑚∠2 + 𝑚∠3 = 180𝑜
1.
2.
3.
4.
5.
6.
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
47𝑜
98𝑜
𝑥, 𝑧, 𝑦
𝑝, 𝑛, 𝑚
Start with the small triangle
𝑓, 𝑒, 𝑔
𝐶𝑜𝑛𝑡𝑖𝑛𝑢𝑒 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑙𝑎𝑟𝑔𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒
𝑔, ℎ, 𝑑
95𝑜
112𝑜
𝐿𝑖𝑛𝑘 𝑡ℎ𝑒 𝑙𝑖𝑠𝑡 𝑡𝑜𝑔𝑒𝑡ℎ𝑒𝑟
𝑓, 𝑒, 𝑔, ℎ, 𝑑
Summary
• What is the sum of all of the angles on the interior of a
triangle?
• The longest side is opposite which angle in a triangle?
• The smallest angle is opposite which side in a triangle?
Formative Assessment
• Skills Practice 5.2
• Pg. 483-485 (1-12)