4.2 /4.3 – Triangle Congruence

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# 4.2 /4.3 – Triangle Congruence - PowerPoint PPT Presentation

4.2 /4.3 – Triangle Congruence. Triangle Congruence. Before … … to prove figures congruent you must show ALL corresponding sides and angles are congruent Now … … we have some shortcuts for TRIANGLES. Shortcut #1. SSS ~ S ide- S ide- S ide

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## 4.2 /4.3 – Triangle Congruence

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### 4.2 /4.3 – Triangle Congruence

Triangle Congruence
• Before …
• … to prove figures congruent you must show ALL corresponding sides and angles are congruent
• Now …
• … we have some shortcuts for TRIANGLES
Shortcut #1
• SSS ~ Side-Side-Side
• If the triangles have three sets of congruent sides, the triangles are congruent (I don’t know any angles)

10

10

5

8

8

5

“INCLUDED”
• What does it mean to be an included angle or an included side?

X

C

7 in

40°

Y

5 in

55°

A

B

Z

“Included”
• An included angle is between two sides (the rays that make the angle would be the sides)
“Included”
• An included side is between two angles (the endpoints of the side would be the vertices of the angles)
Shortcut #2
• SAS ~ Side-(included)Angle-Side
• If the triangles have 2 sets of congruent sides and a set of congruent included angles, then the triangles are congruent

7

70°

4

4

70°

7

Shortcut #3
• ASA ~ Angle-(included) Side-Angle
• If the triangles have 2 sets of congruent angles and a set of congruent included sides, then the triangles are congruent

80°

70°

3

3

70°

80°

Shortcut #4
• AAS ~ Angle-Angle-Side
• If the triangles have two sets of congruent angles and a set of congruent sides, then the triangles are congruent

12

80°

70°

70°

80°

12

Right Triangle Congruence (shortcut #5)
• If the triangles are RIGHT triangles, there is another option …
• HL ~ Hypotenuse-Leg

5

8

13

13

10

10

8

5

Incorrect Congruence Postulates
• These ways DON’T work!
• AAA (AAAAAAAAgggghhhh) doesn’t work
• ASS (if you can’t say it, you can’t use it!)
• This is the same as SSA – that doesn’t work either