Question

Do you know the answer? Help!

Given: ∠D ≅∠T, ∠E ≅ ∠U, EO ≅ UX
Name the postulate or theorem you can use to prove the triangles congruent.

A. SSS Postulate
B. SAS Postulate
C. ASA Postulate
D. AAS Theorem

Answer 1

A cannot be right, as you do not know all 3 sides are equal, you only know one side is.
B cannot be right, as again you only have one side, and need 2
C could be right, but the order is not correct. The side we know is not between the two angles, making this theory incorrect
D is correct, as we have 2 angles next to each other, and a side that is congruent

Answer 2

Answer: D. AAS Theorem

Explanation:

Given: ∠D ≅∠T, ∠E ≅ ∠U, EO ≅ UX

Then in Δ DOE and Δ TXU

∠D ≅∠T, [Angle]

∠E ≅ ∠U, [Angle]

EO ≅ UX [Side]

From the figure we can see they are two pair of corresponding congruent angles and one non included sides.

Thus by AAS theorem

Δ DOE ≅ Δ TXU

• AAS theorem tells that if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.