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4.2 /4.3 – Triangle Congruence

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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  1. 4.2 /4.3 – Triangle Congruence

  2. Triangle Congruence • Before … • … to prove figures congruent you must show ALL corresponding sides and angles are congruent • Now … • … we have some shortcuts for TRIANGLES

  3. 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

  4. “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

  5. “Included” • An included angle is between two sides (the rays that make the angle would be the sides)

  6. “Included” • An included side is between two angles (the endpoints of the side would be the vertices of the angles)

  7. 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

  8. 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°

  9. 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

  10. 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

  11. 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

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