This document discusses congruence in geometry. It defines congruent figures as those where corresponding sides are equal in length and corresponding angles are equal in measure. The conditions for congruence are: (1) all sides of one figure are equal to the corresponding sides of the other, (2) the angles of one figure are equal to the corresponding angles of the other, and (3) the shapes of both figures are the same. Methods for proving triangles are congruent include side-side-side, side-angle-side, and angle-side-angle. An example problem demonstrates using corresponding angles and sides to prove two triangles are congruent.

1. Congruence
 Congruent
•The Conditions
• Congruent Triangles
• How to prove that
• Exercise’s example
Click what you want
to learn

2. Conditions of Congruent
a) The all sides of
corresponding sides are
equal The Conditions for
b) The angles of Congruent of
Corresponding sides Two Plane Figures are:
are equal
c) The shapes of both
figure are same

3. Conditions of Congruent
The example:
A D a) The Corresponding sides
a)
(look the same sign) are:
C B F E AC with DF, AB with
R U V DE, and BC with EF
b)
b) Equal angle of
S T Corresponding side:
W <R with <W, <S with
c)
<V, and <T with <U
c) Both of Plane Figures are
Triangle

4. Prove Congruent Figures
To Prove that 2 Triangles are
Congruent:
A 6cm a) Side, Side, Side
T U
The all sides are in equal
7cm 7cm 5cm
5cm
B S
C 6cm

5. Prove Congruent Figures
To Prove that 2 Triangles are
Congruent:
A 6cm
U b) Two Sides, One Angle
T 45 The angle coincided by two
7cm 7cm sides (AB and BC or UT
and TS)
45 B
6cm
S
C

6. Prove Congruent Figures
A 6cm To Prove that 2 Triangles are
T 45 90
U
Congruent:
c) Two Angles, One Side
45
1. The angles known on the
90 B S
C 6cm side
A 6cm 2.The side face to one of two
T 90 U
55 angles
55
90 6cm B S
C

7. Example
Answer:
We prove it based on the
condition, that we have learn
before. We look for the same
C
B
sign: E
• <CAE equal to <EBD
• CE equal to ED A
• <CEA equal to <BED (It hasn’t D
sign, but it’s vertical angles
Prove that ACE and BDE
The Conclusion: ACE are congruent
and BDE are congruent