Question

which congruence theorem can be used to prove $\triangle bda \cong \triangle dbc$? diagram of triangles with right angles at d and b, marked sides \bigcirc hl \bigcirc sas \bigcirc aas \bigcirc sss

Explanation:

Step1: Identify right angles

Both $\triangle BDA$ and $\triangle DBC$ are right triangles (right angles at $D$ and $B$ respectively).

Step2: Identify equal hypotenuse and leg

• Hypotenuse: $BD$ is common to both triangles, so $BD = BD$ (reflexive property).
• Leg: The marked sides (the legs with the tick marks) are equal, say $AD = BC$ (from the diagram's markings).
• For right triangles, the Hypotenuse - Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Answer:

HL (The HL congruence theorem can be used since we have two right triangles with a common hypotenuse ($BD$) and one pair of equal legs (the marked sides), satisfying the HL criteria for congruence of right triangles.)