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Lesson Menu Five-Minute Check (over Lesson 4–1) Then/Now New Vocabulary Theorem 4.1: Triangle Angle-Sum Theorem Proof: Triangle Angle-Sum Theorem Example 1: Real-World Example: Use the Triangle Angle-Sum Theorem Theorem 4.2: Exterior Angle Theorem Proof: Exterior Angle Theorem Example 2: Real-World Example: Use the Exterior Angle Theorem Corollaries: Triangle Angle-Sum Corollaries Example 3: Find Angle Measures in Right Triangles

Over Lesson 4–1 A.A B.B C.C D.D 5-Minute Check 1 A.acute B.equiangular C.obtuse D.right Classify ΔRST.

Over Lesson 4–1 A.A B.B C.C D.D 5-Minute Check 2 A.8 B.10 C.12 D.14 Find y if ΔRST is an isosceles triangle with RS  RT. ___

Over Lesson 4–1 A.A B.B C.C D.D 5-Minute Check 3 A.2 B.4 C.6 D.8 Find x if ΔABC is an equilateral triangle.

Over Lesson 4–1 A.A B.B C.C D.D 5-Minute Check 4 A.ΔABC B.ΔACB C.ΔADC D.ΔCAB

Over Lesson 4–1 1.A 2.B 3.C 5-Minute Check 5 A.scalene B.isosceles C.equilateral Classify ΔMNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15.

Over Lesson 4–1 1.A 2.B 3.C 4.D 5-Minute Check 6 A.acute B.scalene C.isosceles D.equiangular Which is not a classification for ΔFGH?

Then/Now You classified triangles by their side or angle measures. (Lesson 4–1) Apply the Triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Vocabulary auxiliary line exterior angle remote interior angles flow proof

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Example 1 Use the Triangle Angle-Sum Theorem SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. UnderstandExamine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that  1 and  2 are vertical angles.

Example 1 Use the Triangle Angle-Sum Theorem Triangle Angle-Sum Theorem Simplify. Subtract 117 from each side. PlanFind m  1 first because the measure of two angles of the triangle are known. Use the Vertical Angles Theorem to find m  2. Then you will have enough information to find the measure of  3. Solve

Example 1 Use the Triangle Angle-Sum Theorem Triangle Angle-Sum Theorem Simplify. Subtract 142 from each side.  1 and  2 are congruent vertical angles. So, m  2 = 63. Answer: Therefore, m  1 = 63, m  2 = 63, and m  3 = 38. CheckThe sums of the measures of the angles in each triangle should be 180. m  = or 180 m  2 + m  = or 180

A.A B.B C.C D.D Example 1 A.95 B.75 C.57 D.85 Find the measure of  3.

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Example 2 Use the Exterior Angle Theorem GARDENING Find the measure of  FLW in the fenced flower garden shown. m  LOW + m  OWL= m  FLWExterior Angle Theorem x + 32= 2x – 48Substitution 32= x – 48Subtract x from each side. 80= xAdd 48 to each side. Answer: So, m  FLW = 2(80) – 48 or 112.

A.A B.B C.C D.D Example 2 A.30 B.40 C.50 D.130 The piece of quilt fabric is in the shape of a right triangle. Find the measure of  ACD.

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Example 3 Find Angle Measures in Right Triangles Find the measure of each numbered angle. If 2  s form a linear pair, they are supplementary. Exterior Angle Theorem m  1 = Simplify. = 104 Substitution m  2 = 180 Subtract 104 from each side. 76

Example 3 Find Angle Measures in Right Triangles Subtract 132 from each side. 48 Simplify m  4 = 180 Substitution m  4 = 180 Triangle Sum Theorem (90 – 34) + m  2 + m  4 = 180 Simplify. = 42 If 2  s form a right angle, they are complementary. m  3 = 90 – 48

Example 3 Find Angle Measures in Right Triangles Subtract 131 from each side. 49 Simplify. m  = 180 Triangle Angle-Sum Theorem m  = 180 m  1 = 104, m  2 = 76, m  3 = 42, m  4 = 48, m  5 = 49

A.A B.B C.C D.D Example 3 A.50 B.45 C.85 D.130 Find m  3.

End of the Lesson