4.2 /4.3 – Triangle Congruence

Triangle Congruence Before … Now … … 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