8.4 Similar Triangles This can be written from the similarity statement (without even looking at the picture!) In similar polygons, all corresponding angles.

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Presentation transcript:

8.4 Similar Triangles This can be written from the similarity statement (without even looking at the picture!) In similar polygons, all corresponding angles are congruent. In similar polygons, all corresponding sides are proportional. Use the scale factor

Use the diagram to complete the following: Solutions: LMN 4. 15, x LM; MN; NL 5. 16 15, y 6. 24

Angle-Angle (AA~) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. Use AA~ to prove triangles are similar!

Determine whether the ∆’s can be proved similar Determine whether the ∆’s can be proved similar. If so, write a similarity statement. If not, explain why. 1. 2. 3.

Find the value of the variable. First, find the scale factor. Now, use a proportion to solve for x.

In the diagram, ∆BTW ~ ∆ETC. Write the statement of proportionality. Find m<TEC. Find ET and BE. T 34° E C 3 20 79° B W 12

Similar Triangles Given the triangles are similar. Find the value of the variable. Left side of sm Δ Base of sm Δ Left side of lg Δ Base of lg Δ = 6 5 > 2 6h = 40 > h

Given two triangles are similar, solve for the variables. 14 16 15 ) ) 10 15(a+3) = 10(16) 15a + 45 = 160 15a = 115

∆ABC ~ ∆DBE. Solve for x A 5 D y 9 x B C 8 E 4