### Notes 19 - Proving Triangles Congruent

```Notes 19 – Sections 4.4 & 4.5

Students will understand and be able to use
postulates to prove triangle congruence.

If three sides of one triangle are congruent to
three sides of a second triangle, then the
triangles are congruent.

If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of a second triangle, then the
triangles are congruent.

If two angles and the included side of one
triangle are congruent to two angles and the
included side of a second triangle, then the
triangles are congruent.

If two angles and the non-included side of
one triangle are congruent to the
corresponding two angles and side of a
second triangle, then the triangles are
congruent.

If the hypotenuse and a leg of one right
triangle are congruent to the hypotenuse and
corresponding leg of another right triangle,
then the triangles are congruent.

Side-Side-Angle does not prove congruence.

Angle-Angle-Angle does not prove
congruence.
M
N
Given: MN ≅ PN and LM ≅ LP
Prove: LNM ≅ LNP.
L
Statement
MN ≅ PN and LM ≅ LP
LN ≅ LN
LNM ≅ LNP
Reason
Given
Reflexive property
By SSS
P

Once you prove that triangles are congruent,
you can say that “corresponding parts of
congruent triangles are congruent (CPCTC).
W
Given: WX ≅ YZ and XW//ZY.
Prove: ∠XWZ ≅ ∠ZYX.
Statement
WX ≅ YZ and XW//ZY
XZ ≅ ZX
∠WXZ ≅ ∠YZX
XWZ ≅ ZYX
∠XWZ ≅ ∠ZYX
X
Z
Y
Reason
Given
Reflexive property
Alt. Int. Angles (AIA)
By SAS
By CPCTC
K
J
Given: ∠NKL ≅ ∠NJM
and KL ≅ JM
Prove: LN ≅ MN
Statement
∠NKL ≅ ∠NJM & KL ≅ JM
∠JNM ≅ ∠KNL
JNM ≅ KNL
LN ≅ MN
L
M
N
Reason
Given
Reflexive property
By AAS
By CPCTC
B
Given: ∠ABD ≅ ∠CBD
Prove: AB ≅ CB.
A
∠ABD ≅ ∠CBD
Given
Given
BD ≅ BD
reflexive prop.
ABD ≅ CBD
by ASA
D
C
AB ≅ CB
by CPCTC
Worksheet 4.4/4.5b
Unit Study Guide 3
```