Download ANGRTHRMN **When doing proofs involving overlapping triangles

Congruent Triangles
section 4-4
Geometric figures are congruent if they are the same size and same shape.
Corresponding angles and corresponding sides are in the same position in
polygons with an equal number of sides.
Two polygons are congruent polygons if and only if their corresponding
angles and sides are congruent. Thus, triangles that are the same size and
shape are congruent.
To name a polygon, write the vertices in consecutive order. For example, you
can name polygon PQRS as QRSP or SRQP, but not as PRQS.
In a congruence statement, the order of the vertices indicates the corresponding parts.
Helpful Hint
When you write a statement such as ABC
DEF, you
are also stating which parts of the triangle are congruent.
problem # 1 - In the quilt shown below, SRT
ANG. Name all of the
corresponding angle pairs and all of the corresponding side pairs.
T
G
R
N
S
A
problem # 2 - Given that
EFH
GFH,
a. Find the value of x.
b. Find m
F
GFH
E
(6x - 12)
22
G
H
problem # 3 - Prove that the triangles below are congruent.
Given:
P and
Q
M are right angles
R is the midpoint of PM
PQ
Prove:
MN; QR
PQR
1.
P and
2.
P
NR
3.
PRQ
Q
1.
2.
MRN
3.
N
4.
5. R is the midpoint of PM
5.
6. PR
MR
6.
7. PQ
MN; QR
8.
M
N
M are right angles
M
4.
R
P
MNR
PQR
NR
7.
8.
MNR
**When doing proofs involving overlapping triangles, it is often useful to separate
the triangles and redraw them as shown below:
3.2
3
3.2
1.8
3
1.8
1.5
5
3
problem # 4
Given: JK
Prove:
KL; ML
JKL
KL;
KLJ
N
LKM; JK
1.
2.
3.
JKL
MLK
3.
4.
KLJ
LKM
4.
5.
KJL
LMK
5.
ML; JL
7. KL LK
8. JKL
MK
6.
7.
MLK
K
L
MLK
1. JK KL; ML KL
2. JKL and MLK are rt. angles
6. JK
J
M
The bars that give structural support
to a wooden gate form triangles.
Since the angle measures and the
lengths of of the corresponding
sides are the same, the triangles
must be congruent. Use this
information to do a formal proof.
3
4
4
1.5
2.5
5
8.
ML; JL
MK