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Transcript
Triangle Congruence Proving Triangles Congruent Side-Side-Side (SSS) Postulate Side-Angle-Side (SAS) Postulate Non-example of SAS • Why can’t we use SAS to show these triangles congruent? • The angle in the second triangle is not between the two sides! Not SAS! Angle-Side-Angle (ASA) Postulate Assumptions • Sometimes we have to mark assumptions • Assumptions are things that we know are true, but the figure might not immediately give us this information for free – we have to think about it! Assumption #1 – Reflexive Property • If two triangles share a side, that side is congruent to itself! • SSS Assumption #2 – Third Angle • If two pairs of corresponding angles are congruent, then the third pair is also congruent! • Why? Triangle Angle Sum Theorem says the measures of the angles have to sum to 180! • ASA Assumption #3 – Vertical Angles • Vertical angles are congruent! • ASA Assumption #4 – Third Side of a RIGHT Triangle • If two pairs of corresponding sides are congruent in a RIGHT TRIANGLE, then the third pair is also congruent! • Why? Pythagorean Theorem states that a2+b2=c2. This can only be true if a, b, and c are the same in both triangles. • SSS
