Transcript 8.3 Methods of proving

Warm Up
W
P
∆PRB~ ∆WNM
R
B
N
M
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
A
(AA)
B
E
Given: LP  EA; N is the midpoint of
LP.
P and R trisect EA.
Prove: ∆PEN ~ ∆PAL
L
N
E
SAS ~
P
R
A