9.2/9.3 Similar Triangles and Proportions Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures. Warm-up (IN) 1. Name the triangles that appear to be similar. Assume the triangles in #1 are similar. 2. Write 2 true proportions. 3. If AB=6, AE=8 and AC=7, find AD. 4. If CD=12, AD=15 and BE=10, find AE. A B D E C 15 Minutes - The first part of the warm-up will be a review of the last lesson, and the 2nd is an algebra review to prepare the students for the algebra that will be done in the notes and homework with isosceles triangles. 20 minutes – Check answers to even problems from HW, then to over any questions.

Notes 3 ways to prove triangles are similar! AA Similarity Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures. Notes 3 ways to prove triangles are similar! AA Similarity 2 Corresponding angles are congruent SAS Similarity 2 Corresponding sides are in proportion The included angle is congruent 41 minutes for notes Essential Questions: What is the isosceles triangle theorem and it’s converse? SSS Similarity 3 Corresponding sides are in proportion

Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures. EX 1 – H K L N M Essential Questions: How can you use the Isosceles triangle theorem to write a paragraph proof? CKC p. 456!

Triangle Proportionality Thm Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures. Triangle Proportionality Thm If a segment is // to one side of a triangle and intersects the other 2 sides, then it divided those sides proportionally. D A E C Essential Questions: What are the median and altitude of a triangle? N

the segment is // to the 3rd side and half as long Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures. Midsegment Thm If the midpoints of 2 sides of a triangle are joined by a segment, then L the segment is // to the 3rd side and half as long H A G Essential Questions: How are the median, altitude and angle bisector related in an isosceles triangle? U Properties of Proportions See p. 463

EX 2 – Find each value D A E C N CKC p. 464 on paper! 6 9 Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures. EX 2 – Find each value D 6 A 9 E C N CKC p. 464 on paper!

Out – Describe 3 ways to show two triangles are similar. Summary – Now I’m thinking… HW – p. 456 #1-7, p. 464 #1-6,14-16,21 5 minutes for Summary and closing questions. I will have the students do the Out as a ticket out.