Question

Determine if both triangles are congruent or not. Label the triangles as SSS, AAS, ASA, SAS, HL, or not enough information.

Answer 1

Answer: ASA (angle side angle)

The diagram is not drawn to scale and it appears misleading since AD appears shorter than DC. However, the smaller triangles are congruent and we can prove it using ASA.

The tickmarks on the angles show we have a pair of congruent angles. The other pair of congruent angles are the two right angles (angle BDC and angle ADB). The pair of congruent sides are DB = DB. We use the reflexive property here. The sides are between the congruent angles mentioned. So we'll use ASA and not AAS.

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Extra info:

• We can't use SSS because we only have info about one pair of sides. SAS won't be used either for the same reason.
• HL = hypotenuse leg, and it applies to right triangles only. We don't have any info about the hypotenuse of either triangle, so we can't use this either.

Answer 2

△ABD and △BCD are congruent as:

∠CBD = ∠ABD (Equal Angles)

BD = BD (Common side)

The 90 degree angle (Common between both triangles)

Therefore

△ABD ≅ △BCD (By AAS)