Five-Minute Check (over Lesson 3) Mathematical Practices 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 Lesson Menu

What is coordinate of the image of the point (3, –4) after a reflection in the y-axis? B. (–3, –4) C. (3, 4) D. (4, 3) 5-Minute Check 1

CD has endpoints C(–1, 6) and D(3, 4) CD has endpoints C(–1, 6) and D(3, 4). What are the coordinates of the image of point C after a rotation of 90° about the origin? A. C’(–6, –1) B. C’(1, –6) C. C’(6, –1) D. C’(6, 1) 5-Minute Check 1

This figure does not line symmetry. State whether the figure appears to have line symmetry. If so, how many lines of symmetry does it have? A. yes; 8 lines B. yes; 4 lines yes; 2 lines This figure does not line symmetry. 5-Minute Check 2

The figure has rotational symmetry The figure has rotational symmetry. State the order and magnitude of symmetry. A. 8; 60° B. 8; 45° C. 10; 45° D. 10; 36° 5-Minute Check 4

Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. Content Standards G.CO.10 Prove theorems about triangles. MP

You classified triangles by their side or angle measures. Apply the Triangle Angle-Sum Theorem. Apply Exterior Angle Theorem. Then/Now

remote interior angles flow proof corollary auxiliary line exterior angle remote interior angles flow proof corollary Vocabulary

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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. Understand Examine 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

Triangle Angle-Sum Theorem Use the Triangle Angle-Sum Theorem Plan Find 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 Triangle Angle-Sum Theorem Simplify. Subtract 117 from each side. Example 1

1 and 2 are congruent vertical angles. So, m2 = 63. Use the Triangle Angle-Sum Theorem 1 and 2 are congruent vertical angles. So, m2 = 63. Triangle Angle-Sum Theorem Simplify. Subtract 142 from each side. Answer: Therefore, m1 = 63, m2 = 63, and m3 = 38. Check The sums of the measures of the angles in each triangle should be 180. m1 + 43 + 74 = 63 + 43 + 74 or 180 m2 + m3 + 79 = 63 + 38 + 79 or 180 Example 1

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

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

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

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Find the measure of each numbered angle. Find Angle Measures in Right Triangles Find the measure of each numbered angle. Exterior Angle Theorem m∠1 = 32 +38 Simplify. = 70 If 2 s form a linear pair, they are supplementary. Substitution 70 + m2 = 180 Subtract 70 from each side. 110 Example 3

Exterior Angle Theorem m∠3 + 64 = m∠2 Find Angle Measures in Right Triangles Exterior Angle Theorem m∠3 + 64 = m∠2 Substitution m∠3 + 64 = 110 Subtract 64 from each side. m∠3 = 46 Exterior Angle Theorem m∠5 + 41 = m∠3 + 32 Substitution m∠5 + 41 = 46 + 32 Simplify. m∠5 + 41 = 78 m∠5 = 37 Subtract 41 from each side. Example 3

Triangle Angle-Sum Theorem m∠4 + m∠5 + 41 = 180 Find Angle Measures in Right Triangles Triangle Angle-Sum Theorem m∠4 + m∠5 + 41 = 180 Substitution m∠4 + 37 + 41 = 180 Simplify. m∠4 + 78 = 180 Subtract 132 from each side. 102 m1 = 70, m2 = 110, m3 = 46, m4 = 102, m5 = 37 Example 3

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