Question

prove the following statement using the given pieces of information.
given: ∠wkh ≅ ∠dkh, kh ⊥ wd
prove: △hdk ≅ △hwk
∠wkh ≅ ∠dkh
because it is one of the given pieces of information.
because right angles are congruent.
by the third angles theorem.
because they are alternate interior angles.

Explanation:

We are given that \(KH\perp WD\), so \(\angle HMD=\angle HMW = 90^{\circ}\). In \(\triangle HDK\) and \(\triangle HWK\), we already know \(\angle WKH\cong\angle DKH\) (given) and \(KH = KH\) (common side). For the right - angled triangles \(\triangle HDK\) and \(\triangle HWK\), the right angles (\(\angle HMD\) and \(\angle HMW\)) are congruent. When proving triangle congruence, if we have two angles and a non - included side (AAS - Angle - Angle - Side) or other congruence criteria. Here, the fact that \(\angle WKH\cong\angle DKH\) is given.

Answer:

because it is one of the given pieces of information.