Over Lesson 4 1 BELLRINGER 1 Classify RST

Over Lesson 4– 1 BELLRINGER: 1) Classify ΔRST. 2) Find y if ΔRST is an isosceles triangle with RS RT.

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.

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.

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

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

Use the Exterior Angle Theorem GARDENING Find the measure of FLW in the fenced flower garden shown. m LOW + m OWL = m FLW x + 32 = 2 x – 48 Exterior Angle Theorem 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.

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

Find Angle Measures in Right Triangles Find the measure of each numbered angle. Exterior Angle Theorem m 1 = 48 + 56 Simplify. = 104 + m 2 = 180 76 If 2 s form a linear pair, they are supplementary. Substitution Subtract 104 from each side.

Find Angle Measures in Right Triangles If 2 s form a right angle, they are complementary. m 3 = 90 – 48 Simplify. = 42 (90 – 34) + m 2 + m 4 = 180 56 + 76 + m 4 = 180 132 + m 4 = 180 48 Triangle Angle-Sum Theorem Substitution Simplify. Subtract 132 from each side.

Find Angle Measures in Right Triangles m 5 + 41 + 90 = 180 m 5 + 143 = 180 49 Triangle Angle-Sum Theorem Simplify. Subtract 131 from each side. m 1 = 104, m 2 = 76, m 3 = 42, m 4 = 48, m 5 = 49

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