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### MWA 10 6.4 Similar Triangles

• 1. Similar Triangles Slide 1 Points to remember: • The sum of the angles of a triangle is 180 • If two corresponding angles in two triangles are equal, the third angle will also be equal. • Two triangles are similar if o any two of the three corresponding angles are congruent o or one pair of corresponding angles is congruent and the corresponding sides adjacent to the angles are proportional. • Two right triangles are similar if one pair of corresponding angles is congruent.
• 2. Slide 2 Example 1: If DCE ~ VUW, find the measure of .CD
• 3. Slide 3 Example 1: If DCE ~ VUW, find the measure of .CD List the corresponding sides: and and and DC VU DE VW CE UW
• 4. Slide 4 Example 1: If DCE ~ VUW, find the measure of .CD List the corresponding sides: and and and DC VU DE VW CE UW Set up the proportion and solve… 12 9 36 x  12 324x  1 12 12 2 324x  27x  OR 36 12 9 x  324 12x 3 12 12 24 12x  27x 
• 5. Slide 5 Example 2: The triangles are similar. Calculate the missing side. If 42 and 30, then 12FH RH FR   12 Let x = length of 𝐹𝑆 12 84 42 x  42 1008x  42 10 42 42 08x  24x 
• 6. Slide 6 Example 2: The triangles are similar. Calculate the missing side. If 42 and 30, then 12FH RH FR   12 Let x = length of 𝐹𝑆 12 84 42 x  42 1008x  42 10 42 42 08x  24x  24 FS SG FG  24 84SG  60SG  Answer: The missing side has a measure of 60.
• 7. Slide 7 10.5 Example 3: ABC ~ DEF. Find the missing sides and missing angles.
• 8. Slide 8 10.5 Example 3: ABC ~ DEF. Find the missing sides and missing angles. Since the triangles are similar, the corresponding angles are congruent. 82 A D A       34 C F F       Angles in a triangle add up to 180 180 82 34 180 64 A B C B B               
• 9. Slide 9 10.5 Example 3: ABC ~ DEF. Find the missing sides and missing angles. Since the triangles are similar, the corresponding angles are congruent. 82 A D A       34 C F F       Angles in a triangle add up to 180 180 82 34 180 64 A B C B B                Corresponding sides are proportional. Set up the proportion… 10.5 7 12 y  7 126y  18y  10.5 7 14 z  7 147z  21z 
• 10. Slide 10 Example 4: Tom wants to find the height of a tall evergreen tree. He places a mirror on the ground and positions himself so that he can see the reflection of the top of the tree in the mirror. The mirror is 0.7 m away from him and 5.5 m from the tree. If Tom is 1.8 m tall, how tall is the tree? Note: the triangles are similar.
• 11. Set up the proportion and solve… Slide 11 Example 4: Tom wants to find the height of a tall evergreen tree. He places a mirror on the ground and positions himself so that he can see the reflection of the top of the tree in the mirror. The mirror is 0.7 m away from him and 5.5 m from the tree. If Tom is 1.8 m tall, how tall is the tree? Note: the triangles are similar. Answer: The tree would be 14.14 m tall. 1.8 0.7 5.5h  0.7 9.9h  0.7 0.7 9 .7 .9 0 h  14.14h 
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