Question

in the figure shown, abcd ~ fghj. select all pairs of congruent angles.
a) ∠a≅∠f
b) ∠d≅∠g
c) ∠b≅∠g
d) ∠c≅∠h
e) ∠d≅∠j
f) ∠b≅∠j

Explanation:

Step1: Recall similarity property

For similar polygons, corresponding angles are congruent. Since \(ABCD\sim FGHJ\), \(\angle A\) corresponds to \(\angle F\), \(\angle B\) corresponds to \(\angle G\), \(\angle C\) corresponds to \(\angle H\), and \(\angle D\) corresponds to \(\angle J\).

Step2: Check each option

A) \(\angle A\cong\angle F\) is correct as they are corresponding angles.
B) \(\angle D\cong\angle G\) is incorrect as \(\angle D\) corresponds to \(\angle J\) and \(\angle G\) corresponds to \(\angle B\).
C) \(\angle B\cong\angle G\) is correct as they are corresponding angles.
D) \(\angle C\cong\angle H\) is correct as they are corresponding angles.
E) \(\angle D\cong\angle J\) is correct as they are corresponding angles.
F) \(\angle B\cong\angle J\) is incorrect as \(\angle B\) corresponds to \(\angle G\) and \(\angle J\) corresponds to \(\angle D\).

Answer:

A. \(\angle A\cong\angle F\)
C. \(\angle B\cong\angle G\)
D. \(\angle C\cong\angle H\)
E. \(\angle D\cong\angle J\)