4.1: Congruent Figures
There’s
There’s no
no crying
crying in
in baseball!
baseball!
-Jimmy
Congruent Figures
Congruent Polygons: Congruent polygons are polygons that have
corresponding sides that are congruent and corresponding angles
that are congruent.
C corresponds to R
B corresponds to Q
AX corresponds to PY
B  Q C  R A  P X  Y

AX  PY
XB  YQ
BC QR
ACBX  PRQY





CA  RP
Congruent Figures
To be congruent shape must have the same:
 Shape
 Size
ABC  QRS. List the congruent corresponding parts.
Congruent Figures
Given that the following pentagons are congruent, find the
value of B.
C
A
R
W
132°

B
E
95°
S
P
T
D
Congruent Figures
Given that MNPQR  STUVW find the measure of the
missing angles.
Congruent Figures
Find the measure of the given angles or lengths of the
given sides.
ABC  DEF
1) A  x  120 and D  4 x
2) BC  4 x  17 and EF  2 x  25
Congruent Figures
92°
40°
Theorem 4-1: If two angles of one triangle are congruent to
two angles of another triangle, then the third angles are
congruent.
C  F

Congruent Figures
Decide whether the triangles are congruent. Justify!
E
3
B
4
C
3
A
4
D
Proving Triangles Congruent
Given : AB  CB
Prove : ABD  CBD
AD  CD
BD bisects ABC and ADC
Statements
Reasons
1. AB  CB, AD  CD
1.
2. BD  BD
2.
3. BD bisects ABC and ADC
4. ABD  CBD
ADB  CDB
5. A  C
3.
6. ABD  CBD
4.
5.
6.
Proving Triangles Congruent
Given : PS  PQ
Prove : PQR  PSR
QR  SR
Q  S
QPR  SPR
Statements
Reasons
1. PS  PQ ; QR  SR
1.
2.
2. Reflexive Property
3. Q  S ;QPR  SPR
3.
4. QRP  SRP
4.
5.
5.
Congruent Figures
Solve the following system of equations.
y  x 1
y  3x  5
Congruent Figures
Solve the following systems of equations.
x  y  11
3x  y  5
5x  3 y  7
3 x  5 y  23
Congruent Figures
Given that the following triangles are congruent, find the
values of the variables.
2y+3
x+y
x
12
4.1: Congruent
Figures
p.200 #3-13,
16-23, 25, 27,
30-34 even, 44
p.234 #1,3,5,8,9
I just like to smile. Smiling’s my favorite!
I just like to smile. Smiling’s my favorite!
-Buddy