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similar triangles April 09, 2015 Warm-Up Dividing a segment proportionally. Find two possible locations for point M that would divide segment AB in a 1:3 ratio. A B (Hint: Side-Splitter Theorem) similar triangles April 09, 2015 Warm-Up Dividing a segment proportionally. Find two possible locations for point M that would divide segment AB in a 1:3 ratio. A 12 8 B (Hint: Side-Splitter Theorem) similar triangles SIMILAR April 09, 2015 TRIANGLES similar triangles April 09, 2015 Unit 7 SUMMARY Lesson 31 - What does "similar" MEAN? Lesson 32 - How do I MAKE similar figures? Lesson 33 - Lesson 34 & - How do I USE similar triangles? Lesson 35 similar triangles April 09, 2015 Unit 7 SUMMARY Lesson 31 - What does "similar" MEAN? Congruent angles & proportional sides Lesson 32 - How do I MAKE similar figures? Dilations! Lesson 33 - Lesson 34 & - How do I USE similar triangles? Lesson 35 To make PROPORTIONS (extended, geometric mean, side-splitter, angle bisector) similar triangles April 09, 2015 Lesson 33 Similar Triangles similar triangles April 09, 2015 SIMILAR TRIANGLES C' C A B A' What can you say about angle C and angle C'? Why? B' similar triangles April 09, 2015 SIMILAR TRIANGLES C' C a A e d b c B a d A' f c b = = e f Are the sides in proportion? B' similar triangles Name FOUR postulates or theorems you learned that can be used to prove two triangles are CONGRUENT. April 09, 2015 similar triangles April 09, 2015 QUESTIONS... 1. If two triangles are SIMILAR, are they also CONGRUENT? 2. If two triangles are CONGRUENT, are they also SIMILAR? similar triangles April 09, 2015 SIMILAR TRIANGLES If TWO ANGLES of one triangle are CONGRUENT to TWO ANGLES of another triangle, then the triangles are SIMILAR. similar triangles April 09, 2015 SIMILAR TRIANGLES If TWO CONGRUENT ANGLES, then the triangles are SIMILAR. similar triangles April 09, 2015 SIMILAR TRIANGLES Example 1: similar triangles April 09, 2015 SIMILAR TRIANGLES Example 1: similar triangles April 09, 2015 SIMILAR TRIANGLES Example 2: similar triangles April 09, 2015 SIMILAR TRIANGLES Example 2: similar triangles April 09, 2015 SIMILAR TRIANGLES Example 3: similar triangles April 09, 2015 SIMILAR TRIANGLES Example 3: similar triangles April 09, 2015 SIMILAR TRIANGLES Example 3: similar triangles April 09, 2015 SIMILAR TRIANGLES GEOMETRIC MEAN: 1) THREE similar triangles are formed (Thm. 7-3) C A B N C 1. A B 2. C A N 3. C N B similar triangles April 09, 2015 SIMILAR TRIANGLES SIDE-SPLITTER Theorem: I H G J K similar triangles April 09, 2015 SIMILAR TRIANGLES If the CORRESPONDING SIDES of two triangles are PROPORTIONAL then the triangles are SIMILAR. similar triangles April 09, 2015 SIMILAR TRIANGLES If CORRESPONDING SIDES PROPORTIONAL, then the triangles are SIMILAR. similar triangles April 09, 2015 SIMILAR TRIANGLES similar triangles April 09, 2015 SIMILAR TRIANGLES If an angle of one triangle is CONGRUENT to an angle of another triangle, and the lengths of the TWO SIDES FORMING those angles are in PROPORTION, then the triangles are SIMILAR. similar triangles April 09, 2015 SIMILAR TRIANGLES TWO SIDES PROPORTIONAL and CONGRUENT INCLUDED ANGLE, then the triangles are SIMILAR. similar triangles April 09, 2015 SIMILAR TRIANGLES similar triangles April 09, 2015 SIMILAR TRIANGLES similar triangles April 09, 2015 Unit 7 SUMMARY Lesson 31 - What does "similar" MEAN? Congruent angles & proportional sides Lesson 32 - How do I MAKE similar figures? Dilations! Lesson 33 - How do I KNOW two triangles are similar? AA ~ Post. SSS ~ Thm. SAS ~ Thm. Lesson 34 & - How do I USE similar triangles? Lesson 35 To make PROPORTIONS (extended, geometric mean, side-splitter, angle bisector)
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