Question

question 2 (5 points)
listen
if ( p perp q ), which of the following statements is true for the given figure?
a) ( angle 1 + angle 4 cong angle 2 + angle 3 )
b) ( angle 1 cong angle 3 )
c) ( angle 1 + angle 2 cong angle 3 + angle 4 )
d) ( angle 1 + angle 3 cong angle 2 + angle 4 )

Explanation:

Step1: Recall perpendicular lines property

Since \( p \perp q \), the angles formed between them are right angles (\( 90^\circ \)). So, \( \angle1 + \angle2 = 90^\circ \) and \( \angle3 + \angle4 = 90^\circ \).

Step2: Analyze each option

• Option A: \( \angle1 + \angle4 \) vs \( \angle2 + \angle3 \). From \( \angle1 + \angle2 = 90^\circ \) and \( \angle3 + \angle4 = 90^\circ \), we can't directly say these sums are equal.
• Option B: \( \angle1 \) and \( \angle3 \) have no direct equality from \( p \perp q \).
• Option C: \( \angle1 + \angle2 = 90^\circ \) and \( \angle3 + \angle4 = 90^\circ \), so \( \angle1 + \angle2 \cong \angle3 + \angle4 \) (both are \( 90^\circ \)).
• Option D: \( \angle1 + \angle3 \) vs \( \angle2 + \angle4 \). No direct equality from \( p \perp q \).

Answer:

C) \( \angle1 + \angle2 \cong \angle3 + \angle4 \)