Warm Up ∆PRB~ ∆WNM PR = 20 PB =18 RB = 22 WN =12 Find NM and WM

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Presentation transcript:

Warm Up ∆PRB~ ∆WNM PR = 20 PB =18 RB = 22 WN =12 Find NM and WM 20/12 = 18/WM = 22/NM WM = 10.8 and NM = 13.2

8.3 Methods of proving triangles similar

Postulate: If there exists a correspondence between the vertices of two triangles such that the three angles of one triangle are congruent to the corresponding angles of the other triangle, then the triangles are similar. (AAA) The following 3 theorems will be used in proofs much as SSS, SAS, ASA, HL and AAS were used in proofs to establish congruency.

T62: If there exists a correspondence between the vertices of two triangles such that two angles of one triangle are congruent to the corresponding angles of the other, then the triangles are similar. (AA) (no choice) T63: If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of corresponding sides are equal, then the triangles are similar. (SSS~)

T64: If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of two pairs of corresponding sides are equal and the included angles are congruent, then the triangles are similar. (SAS~)

Given: ABCD is a Prove: ∆BFE ~ ∆ CFD D C F E A B (AA)

Given: LP  EA; N is the midpoint of LP. P and R trisect EA. Prove: ∆PEN ~ ∆PAL L N A E P R SAS ~