4-2: Congruency Postulates. What do we know about congruency so far? A B C D E F G H All corresponding sides and angles must be equal for the two shapes.

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4-2 Triangle Congruence by SSS and SAS

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Presentation transcript:

4-2: Congruency Postulates

What do we know about congruency so far? A B C D E F G H All corresponding sides and angles must be equal for the two shapes to be congruent!

Side-Side-Side Postulate If the 3 sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. H G F Q R P

Given: HF = HJ, FG = JK, H is the midpoint of GK. ~~ Prove: Triangle FGH = Triangle JKH ~ G F H J K By the midpoint definition, GH = KH ∆FGH = ∆JKH by SSS. ~ ~

Side-Angle-Side (SAS) Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. A B C D E F

From the information given, can you prove Triangle RED = Triangle CAT? Explain. ~ R E D C A T Given: RE = CA, RD = CT, ‹R = ‹T ~ ~ ~ No, cannot prove congruency. ∆CAT does not have the included angle between the two sides. Not SAS.

From the information given, can you prove Triangle AEB = Triangle DBC? Explain. A B C D E Given: EB = CB, AE = DB ~~ By the definition of vertical angles, ‹ABE = ‹DBC. No, cannot prove congruency. ∆AEB does not have the included angle between the two sides. Not SAS. ~