Similar Triangles Notes PDF

Objective 14: Similar Triangles Goal: Find missing angles and sides of similar triangles. Part 1: Solving Ratios & Proportions Ratios and Proportion Word Problems Key Terms Representation...

Objective 14: Similar Triangles Goal: Find missing angles and sides of similar triangles. Part 1: Solving Ratios & Proportions Ratios and Proportion Word Problems Key Terms Representation Definition/Direction ! The comparison of two values expressed as a Ratios a : b, a to b and " fraction. Proportion Two ratios those are equal. Solve for y. 3 2 y +2 8 A = = a) y +2 y b) 7 y+3 5y 50 0 3y 294 y 0 94 11419 Vocabulary Definition Picture Triangles that have congruent Similar Triangles angles and proportional sides. CDICC LET D Corresponding COELA C 2.5 Angles 2 70° (Congruent) and 6 7.5 42° Proportional T 4 A Sides Qa Bla 68° 42° G 12 O The ratio that you get when you divide corresponding side lengths of similar figures. Scale Factor Another way to describe a scale factor is that it's a multiplier. 1) Are triangles △ABC and △DEC similar? Big 6 8 small yes 2) The triangles are similar. a) Given the triangles above, write a similarity statement. ALNM ΔRQP b) Find x and y. 4 8 42 If 5by 5.6 47.6 5 by 532 9.5 1 3) Triangles are similar in the figure below. RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10. a) Given the triangles above, write a similarity statement. Δ UTQ ASRQ b) Find RQ and QT. Big Small 10 308 40 10 QT 2 19 3 RQ 8  Part 2: Parts of Similar Triangles 1) Josh wanted to measure the height of the Willis Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1:00 p.m. The length of the shadow was 2 feet. Then he measured the length of Willis Tower’s shadow and it was 242 feet at the same time. What is the height of the Willis Tower? 2 i 211 452 Ft 2) Write a similarity statement. If so, how long is NP? M N 10 12 P AMNP A MRS 18 15 R X S 20 small big 25 200 8 3) Solve for x, y, and z in the figure below. If necessary, leave answers in simplified fraction form. geometric means 42.67 x = ___________ 40 y = ___________ 169 z = ___________ É 24 322 22 31 24 1024 1 42.665 42.67