8.4 Similar Triangles

Number Talk In Chemistry Class there is a girl to boy ratio of 5 : 8. If there are a total of 39 students, how many boys are there? The scale on a map is 6cm : 2kn. If the distance between two cities is 8kn, how far apart in cm are the two cities on the map? In Geometry Class, the girl to boy ratio is 8 to 6. If there are a total of 42 students, how many girls are there?

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

∆ABC is similar to ∆DBE x y B A C D E

Agenda Number talk expectations Number talk Warm up Discuss the Angle Angle Theorem

Number Talk Name the rule!

Warm Up Given the triangles are similar. Find the value of the variable. ) ) )) m 42

Postulate 25 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.

Determine whether the triangles are similar ° 33° No, because two angles of one triangle are not congruent to two angles of another triangle.

Determine whether the triangles are similar. 60° Yes, because two angles of one triangle are congruent to two angles of another triangle. 60°

Decide whether two triangles are similar, not similar, or cannot be determined. 92°57° 92° 41° A A = 180 A = 180 A = 31 31° S S = 180 S = 180 S = 47 47° Not similar

Given two triangles are similar, solve for the variables. 10 a b - 8 ) ) 15(a+3) = 10(16) 15a + 45 = a = 115

2 Practice Problems For each problem. Show your solutions mathematically as well as explain what you did in plain English. For Example “When setting up the proportion 4/x = 15/5 I knew that EB corresponds with DC and EA corresponds with AD.”

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