1. 7.3 Proving Triangles Similar
Name the postulate or theorem you can use to prove the triangles congruent.
1. 2. 3.
Objectives:
To use the AA ∼ Postulate and the SAS ∼ and SSS ∼ Theorems
To use similarity to find indirect measurements
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2. Essential Understanding
You can show that two triangles are similar when you know the relationships between only two or three pairs of corresponding parts.
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3. Post 7-1 Angle-Angle Similarity (AA~) Postulate
If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the triangles are similar P T L M S R
ΔTRS ~ ΔPLM
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4. Ex. 1 Explain why the triangles are similarV 45 S 45 R B
Is there enough info to write the similarity ratio?
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5. Thm 7-1 Side – Angle –Side Similarity (SAS~)
If an angle of 1 triangle is congruent to an angle of a 2nd triangle and the sides including the 2 angles are proportional, the triangles are similar Q A
If ∠A ≅ ∠Q and C B S R
Then ΔABC ~ ΔQRS
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6. Thm. 7-2 Side – Side – Side Similarity (SSS~)
If the corresponding sides of 2 triangles are proportional, then the triangles are similar.
Click for next slide Q A C B S R If
then ΔABC ~ ΔQRS

7. Ex. 2 Explain why the following triangles are similarb) a) Z P K 6 8 58 58 R A Q X B 3 4 Y X
Given: MX ⊥ AB
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8. c) 9 G A B 6 6 8 8 C F E 12
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9. The lengths of the sides of similar triangles can be found by using Similar Theorems.
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10. Ex. 3 Explain why the triangles are similar and find DE12 10 24 B 16 C 18 E
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11. #3 Find x 12 6 x 8
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12. Indirect measurements
Measurement that would be hard to actually measure.
Can use similar triangles to find these measurements.
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13. What is the Length of JS? (Round to the nearest tenth)
x FT H
6 FT S V T
7 FT
40.5 FT
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14. Classwork
7.3 Review Worksheet
LESSON OVER