Question

prove the following statement using the given pieces of information.
given: ∠kwj ≅ ∠hwj, wj ⊥ kh
prove: △hjw ≅ △kwj
∠xwj ≅ ∠hwj
by the third angles theorem.
because right angles are congruent.
because it is one of the given pieces of information.
because they are alternate interior angles.

Explanation:

Step1: Identify right angles

Since \( WJ\perp KH\), \(\angle HJW=\angle KJW = 90^{\circ}\) (by the definition of perpendicular lines).

Step2: Use given angle equality

Given \(\angle K WJ\cong\angle H WJ\).

Step3: Apply AAS (Angle - Angle - Side) congruence

In \(\triangle HJW\) and \(\triangle KJW\):

• \(\angle HJW=\angle KJW\) (right angles, \(90^{\circ}\))
• \(\angle K WJ\cong\angle H WJ\) (given)
• \(WJ = WJ\) (common side)

By the AAS (Angle - Angle - Side) congruence criterion, \(\triangle HJW\cong\triangle KJW\).

Answer:

\(\triangle HJW\cong\triangle KJW\) (by AAS congruence)