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

RP

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.

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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 proveTriangle RED = Triangle CAT? Explain.~

R E

D

C A

T

Given: RE = CA, RD = CT, ‹R = ‹T

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No, cannot prove congruency.

∆CAT does not have the included angle between the two sides. Not SAS.

From the information given, can you proveTriangle 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.

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