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SECONDARY MATH 2 LESSON CORE STANDARDS II.5.G.SRT.4 II.5.G.SRT.5 5-2 OBJECTIVE 1. SWBAT apply properties of similar triangles to solve problems. Definition of Similar Triangles NOTES ABC ~ XYZ A If two triangles are similar, then corresponding angles are congruent and corresponding sides are proportional. X C B A X, B Y, C Z Z Y Proving Similarity Angle-Angle Similarity Postulate If two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar. Side-Side-Side Similarity Theorem If the three sides of one triangle are proportional to the three corresponding sides in another triangle, then the triangles are similar. Triangle Proportionality Theorem If a line intersects 2 sides of a triangle and is parallel to the third side, then the two intersected sides are divided proportionally. (converse is also true.) C A D E B EXAMPLES 1. If ABC ~ XYZ, find the measure of every missing side or angle. 2. If ABC ~ XYZ, solve for x. C x+5 X 12 B 3. 2x – 2 Z 18 x+7 Y Y 4. Solve for x. x+9 B x–9 x+6 E x – 11 C X B Given AB CD , prove ABE DCE Statements Reasons A Z x+2 15 8 59 C A 85 A D PRACTICE 5-2 NAME______________________________ [SHOW YOUR WORK] Solve for x. 1. ABC ~ XYZ 2. x 5 X C 12 x – 10 A x 35 x–7 15 B Z Y 3. ABC ~ XYZ 4. 2x X x–1 3x – 15 A B 3x + 11 2x + 8 Y 2x – 13 C 4x + 3 x+1 Z Complete the proof. 5. Given AB CD and AC ED Prove that ABC DCE A B Statements Reasons E C D 6. One triangle has side lengths in centimeters of 3, 7 and 8. Another triangle has side lengths in centimeters of 20, 7.5 and 17.5. Are the triangles similar? Show work to justify your answer. 7. Given that TUV RQP , and mT 42 , and T Q , then what is the measure of V ? 8. Given that a = b; Prove that LNM Q N f a c e d L b M LMQ Statements Reasons