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4.2 /4.3 – Triangle Congruence PowerPoint Presentation
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4.2 /4.3 – Triangle Congruence - PowerPoint PPT Presentation


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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 ~ S ide- S ide- S ide

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4.2 /4.3 – Triangle Congruence


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Presentation Transcript
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
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
“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

included1
“Included”
  • An included angle is between two sides (the rays that make the angle would be the sides)
included2
“Included”
  • An included side is between two angles (the endpoints of the side would be the vertices of the angles)
shortcut 2
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
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
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
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
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