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Congruent Triangles
An Introduction to Corresponding Parts
Two figures are congruent if they are the same size and same shape.
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
Corresponding parts are angles and sides that “match.”
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
A X
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
B Y
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
C Z
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
AB XY
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
BC YZ
∆ABC is congruent to ∆XYZ
A B
C
X Y
Z
Corresponding parts of these triangles are congruent.
AC XZ
∆BAD is congruent to ∆THE
B A
D E
T H
Name all corresponding parts.
∆QRS is congruent to ∆BRX
BR
Q
S
X
Name all corresponding parts.
∆EFG is congruent to ∆HFG
H
G
F
E
Name all corresponding parts.
15
Using Corresponding PartsIn the diagram, ΔITP ≅ ΔNGO. Find the values of x and y.
In the figure, quadrilateral JIHK quadrilateral QRST.
Find a.
3a
4b° 6
30°Q
120°R S
H I
J
K c + 10°
T
In the figure, quadrilateral JIHK quadrilateral QRST.
3a
4b° 6
30°Q
120°R S
H I
J
K c + 10°
T
Find b.
In the figure, quadrilateral JIHK quadrilateral QRST.
Find c.
3a
4b° 6
30°Q
120°R S
H I
J
K c + 10°
T
19
Prove That Two Triangles are CongruentWrite a two-column proof.
Prove: ΔLMN ≅ ΔPON
Statements Reasons
Find the missing information in the following proof.
Prove: ΔQNP ≅ ΔOPN
Proof:ReasonsStatements
3. Given3.∠Q ≅ ∠O, ∠NPQ ≅ ∠PNO
2. 2. Reflexive Property of Congruence
5. Definition of Congruent Polygons5. ΔQNP ≅ ΔOPN
4. _________________4. ∠QNP ≅ ∠ONP ?
1. 1. Given
22
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Homework!!
• Pg. 257 (4 - 20, 24, 28 - 30)
