1. Figures that have the same size and shape
∆ABC ≅ ∆DEF
You couldn't say ∆ABC ≅ ∆FDE
because the corresponding parts
don't match. The order corresponding
figures are named matters since
the corresponding parts MUST line
up in the name.
Sides or angles that are in the same place in
congruent figures

2. Objects are often drawn
in different orientations to test your ability to
correctly identify corre-sponding parts.
FGH
∠F ∠G ∠H
FG GH HF
m∠W WX
5x + 5
y - x x
y - 12 12 18

3. ∠F ≅ ∠S
∠G ≅ ∠T
∠H ≅ ∠U
∠J ≅ ∠V
FG ≅ ST
GH ≅ TU
HJ ≅ UV
JF ≅ VS
m∠G = m∠T
2x - 7 = 103
2x = 110
x = 55
m∠G = 2x - 7
m∠G = 2(55) -7
m∠G = 103

4. ∠Q RS ∠4 ∠3
Alternate Int ∠'s Theorem
This is a
paragraph
proof
congruent
RS SP
Reflexive Property
congruent
∆RSP
Yes
size
shape

5. congruent
Vertical Angles Theorem
∠VWU ∠V
180° - 66° - 44° °
70°

6. Remember, the Reflexive
Property is used when a
side or angle is shared
between shapes.
HG ≅ HG
∠F ≅ ∠J
Given
HG ≅ HG
Given
∠F ≅ ∠J
Definition of ≅ ∆'s

7. ∆ABC
∆DEF ≅ ∆ABC
∆ABC ≅ ∆JKL

8. From the diagram, AB ≅ CD. Point E is the midpoint of AC and BD.
Therefore, AE ≅ CE and BE ≅ DE by the definition of midpoint. This means
all the corresponding sides are congruent.
The diagram shows AB ∥ CD, so ∠A ≅ ∠C by the Alt. Int. ∠'s Thm. Also, ∠AEB ≅ ∠CED
by the Vertical ∠'s Thm. All corresponding parts are congruent, so ∆ABE ≅ ∆CDE.
m∠D =
=62
You must also know that AB ≅ DE and BE ≅ CE to
conclude that ∆ABE ≅ ∆DCE.