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Transcript
4 Geometry Triangle Proofs (14).notebook October 24, 2014 CONGRUENT TRIANGLES TWO TRIANGLES ARE CONGRUENT IF: 1. CORRESPONDING SIDES ARE CONGRUENT 2. CORRESPONDING ANGLES ARE CONGRUENT 1 4 Geometry Triangle Proofs (14).notebook October 24, 2014 NOTATION: ABC≅ DEF VERTICES AND SIDES MUST MATCH UP WHEN NAMING CONGRUENT TRIANGLES. 2 4 Geometry Triangle Proofs (14).notebook October 24, 2014 THESE STATEMENT ARE TRUE FOR SHOWING ANY TWO POLYGONS OR SHAPES CONGRUENT. 3 4 Geometry Triangle Proofs (14).notebook October 24, 2014 WOULDN'T IT BE NICE IF WE DIDN'T HAVE TO SHOW ALL 6 THINGS CONGRUENT ON TRIANGLES? happy 4 4 Geometry Triangle Proofs (14).notebook October 24, 2014 WE CAN PROVE TWO TRIANGLES CONGRUENT IF WE CAN MATCH TO THE FOLLOWING POSTULATES AND THEOREMS. THE BIG 5 5 4 Geometry Triangle Proofs (14).notebook October 24, 2014 SIDESIDESIDE CONGRUENCE POSTULATE SSS SIDE ANGLE SIDE CONGRUENCE POSTULATE SAS ANGLE SIDE ANGLE CONGRUENCE POSTULATE ASA ANGLE ANGLE SIDE CONGRUENCE THEOREM AAS HYPOTENUSE LEG CONGRUENCE THEOREM HL 6 4 Geometry Triangle Proofs (14).notebook October 24, 2014 THERE IS NO SUCH THING AS A: AAA POSTULATE OR THEOREM AND THERE DEFINITELY IS NOT A SSA POSTULATE OR THEOREM 7 4 Geometry Triangle Proofs (14).notebook October 24, 2014 THE ORDER IS IMPORTANT. RULE FOR DETERMINING THE BIG 5 NEVER SKIP MORE THAN 1 THING IN THE PICTURE. OK TO SKIP 1 THING good BAD TO SKIP 2 THINGS bad 8 4 Geometry Triangle Proofs (14).notebook October 24, 2014 OUR TWO BEST FRIENDS IN THESE TYPES OF PROOFS ARE: 1. REFLEXIVE PROPERTY OF CONGRUENCE 2. VERTICAL ANGLES ARE CONGRUENT 9 4 Geometry Triangle Proofs (14).notebook October 24, 2014 E B A C D F SSS WE WRITE TRIANGLE ABC ≅ TRIANGLE DEF 10 4 Geometry Triangle Proofs (14).notebook October 24, 2014 b a c d 11 4 Geometry Triangle Proofs (14).notebook a October 24, 2014 c b e d 12 4 Geometry Triangle Proofs (14).notebook October 24, 2014 b a d c 13 4 Geometry Triangle Proofs (14).notebook October 24, 2014 b c a d 14 4 Geometry Triangle Proofs (14).notebook October 24, 2014 p216 228 all (SSS, SAS) p223 113, 1822 all ( AAS, ASA) p239 1116, 33, (HL) 15