Download 8.3 Methods of proving

Methods of
Proving
Triangles
Similar
Lesson 8.3
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 where used in proofs to
establish congruency.
Theorem 62: 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)
Theorem 63: 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~)
Theorem 64: 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~)
D
Given: ABCD is a
Prove: ∆BFE ~ ∆ CFD
1.
2.
ABCD is a
AB ║ DC
3.
CDF  E
4. DFC  EFB
5. ∆ BFE ~ ∆CFD
C
F
A
B
1. Given
2. Opposite sides of a
are ║.
3. ║ lines → alt. int.
s 
4. Vertical s are 
5. AA (3, 4)
E
L
Given: LP  EA
N is the midpoint of LP.
P and R trisect EA.
N
E
P
R
Prove: ∆PEN ~ ∆PAL
Since LP  EA, NPE and LPA are congruent right
angles.
If N is the midpoint, of LP, NP = 1 .
LP 2
But P and R trisect EA so EP = 1 .
PA 2
Therefore, ∆PEN ~ ∆PAL by SAS ~.
A