Definition of Congruence:
Two geometric figures are congruent if they have exactly the same _______________
and same ______________.
There is a correspondence between their angles and sides such that
1.) corresponding angles are congruent
2.) corresponding sides are congruent
ORDER OF THE
LETTERS IS
IMPORTANT!!!
E
B
∆𝑨𝑩𝑪 ≅ ∆𝑫𝑬𝑭
A
C
Corresponding Angles
D
F
Congruent
Figures
All the parts of
one figure are
congruent to the
corresponding
parts of the
other.
Corresponding Sides
Theorem 4.3: Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then
_______________________________________________
Example:
If  A and  B of ∆ABC are congruent to  D and  E of
then _______ ≅ ______.
Reflexive property of congruent triangles:
∆ABC
Symmetric property of congruent triangles: If
∆DEF respectively,
≅ ___________
∆ABC
≅
∆DEF
then _______________
Transitive property of congruent triangles:
If
∆ABC
≅
∆DEF
and
∆DEF
≅
∆JKL
then ____________________
When you are told that 2 figures are
congruent, MARK ‘EM UP!!!
Use the marks to write congruence
statements. Watch your order!
________________________
You decide – is it possible to write a congruence statement? If so, do so in
the correct order.
7.
8.
______________________
______________________
Y
Recall: Isosceles triangle
(Label as much as you can)
Z
X
A
Base Angle Theorem
If two sides of a triangle are congruent, then the opposite
angles are ____________________
If AB ≅ AC, then __________________
A
Converse of Base Angle Theorem
If two angles of a triangle are congruent, then the sides opposite
them are _____________________
If  B ≅  C, then ______________
C
B
B
C
Since the converse of the Base Angle Theorem is true what is the biconditional?
Examples:
1.) In isosceles ∆PQR. With base QR, PQ = 2x+3 and PR = 9x–11. What is the value of x?
Equilateral and Equiangular
If a triangle is _______________, then it is ___________________.
If a triangle is _______________, then it is ___________________.
Biconditional: A triangle is ______________ iff it is __________________.
Name: __________________
1.)
(a)
Block: _____
∆ABC ≅ ∆DEF
B
E
80
 A ≅ ________
A
(b) FD ≅ ________
(c)
Date: _________
∆FDE ≅ ________
2.) Given:
A
35o
C
(d) BA = ________
o
F
8 cm
D
(e) mLA = mL_____ = _____
∆ABC ≅ ∆DEF, find the values of x and y.
F
87o
(3y)°
B
E
42o
(5x + 2)o
D
C
4. Given:  L   X and  J   Y. Find the value of k and m  Z.
(3k -20)o
M Y
J 35o
Z
X
L
H
5.) (a) If HG ≅ HK , then _______ ≅ _______
(b) If  KHJ ≅  KJH, then _______ ≅ _______
G
K
J
6.) Proof:
H
GIVEN: FH  JH , FG  JG
FHG  JHG
FGH  JGH
PROVE: FGH  JGH
F
G
J
Find the unknown measure.
6.)
7.)
8.)
P
?
15
R
Find the values of x and y.
9.)
10.)
11.) Find the perimeter of the triangle.
3
Q
18