Warm ups Classify ΔRST. Find y if ΔRST is an isosceles triangle with RS = RT. ___ Find x if ΔABC is an equilateral triangle.

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Presentation transcript:

Warm ups Classify ΔRST. Find y if ΔRST is an isosceles triangle with RS = RT. ___ Find x if ΔABC is an equilateral triangle.

4-2 ANGLES OF TRIANGLES

Triangle Angle-Sum Theorem

Example SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. Plan:You know that <1 and <2 are vertical angles. Use the Ver. Angles Thm to find m<2. Then you will have enough information to find the measure of <3.

Example Plan***Find m<1 first because the measure of two angles of the triangle are known. So, m<2 = 63. Therefore, m<1 = 63, m<2 = 63, and m<3 = 38.

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

Exterior Angle Theorem

Example Find the measure of <FLW. m<LOW + m<OWL = m<FLW Exterior Angle Thm x + 32= 2x – 48 32= x – 48 80= x Answer: So, m<FLW = 2(80) – 48 = 112.

TWAP 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.

Corollary – statement that can be easily proved using a theorem

Example Find the measure of each numbered angle. Exterior Angle Theorem M<1 = = m<2 =

Example continued m<4 = m< 4 = m<2 + m< 4 = 180 = 42 M< 3 = 90 – 48 Bottom angle: = 56

Example cont 49 m< = 180 m< = 180 m<1 = 104, m<2 = 76, m<3 = 42, m<4 = 48, m<5 = 49 That was a CRAZY one!!!!!!!!!!!

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

Homework Pg. 250 #11-32 all, 46, 50