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
∠khw ≅ ∠khd because perpendicular lines form right angles, and all right angles are congruent
kh and kh are the two pairs of congruent angles
adjacent sides next to
included sides between

Explanation:

Step1: Analyze the given congruent angles

We are given that \(\angle WKH\cong\angle DKH\) and \(\angle KHW\cong\angle KHD\) (since \(KH\perp WD\), right - angles are congruent).

Step2: Consider the side \(KH\)

\(KH\) is a common side to both \(\triangle HDK\) and \(\triangle HWK\). In the Angle - Angle - Side (AAS) or Angle - Side - Angle (ASA) congruence criteria, when we have two pairs of congruent angles, the side's position matters. For the ASA (Angle - Side - Angle) criterion, the side should be between the two angles. Here, \(KH\) is between \(\angle WKH\) and \(\angle KHW\) in \(\triangle HWK\) and between \(\angle DKH\) and \(\angle KHD\) in \(\triangle HDK\).

Answer:

included sides between