Question

consider the proof below.

part a: which of the following correctly fills in statement 2?

part b: which of the following correctly fills in reason 4?

Explanation:

Part A

Step1: Use the Corresponding Angles Theorem

Since \(HW\parallel XB\), when two parallel lines are cut by a transversal \(RB\), the corresponding angles are equal.
For angles \(\angle RWH\) and \(\angle RBX\), because \(HW\parallel XB\) and \(RB\) is the transversal, by the Corresponding Angles Theorem, \(\angle RWH\cong\angle RBX\)

Part B

Step1: Recall the AA (Angle - Angle) similarity criterion

We know that \(\angle HRW\cong\angle XRB\) (given by the Reflexive Property) and \(\angle RWH\cong\angle RBX\) (from Part A).
In two triangles \(\triangle RHW\) and \(\triangle RXB\), if two pairs of corresponding angles are congruent, then the two triangles are similar by the AA (Angle - Angle) similarity criterion.

Answer:

• Part A: \(\angle RWH\cong\angle RBX\)
• Part B: AA -