Identify the triangle congruence postulate or theorem (sss, sas, asa, aas, or hl) that shows the triangles are congruent. if the triangles are not congruent, state not congruent.

answer:

sss, sas, asa, not congruent, asa

step-by-step explanation:

1.

qs = qr

ps = pr

qp = qp   (common arm)

∴ the triangles are congruent by sss rule.

2.

ac = ce

bc = cd

∠acb = ∠dce   (v.o.a)

∴ the triangles are congruent by sas rule.

3.

∠rst = ∠tuv

st = ut

∠rts = ∠utv   (v.o.a)

∴ the triangles are congruent by asa rule.

since it is not given that the hypotenuses are equal, we cannot consider hl (rhs) rule.

4.

since, ssa rule do not exist, we cannot say that they are congruent.

5.

since 2 angles are equal, the third angle will also be congruent by angle sum property.

so,

∠gjh = ∠fgj

jg = jg

∠fjg = ∠jgh

∴ the triangles are congruent by asa rule.

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