Answer:
AC and PR are (3x - 1) cm and (x + 5) cm
Explanation:
The question asks why AABC is equal to APQR and requires finding the lengths of AC and PR.
To determine if AABC is equal to APQR, we need to compare their corresponding angles and sides.
Looking at the given figures, both AABC and APQR have two pairs of congruent angles. In AABC, the angles marked as 120° are congruent, and the angles marked as 30° are congruent. Similarly, in APQR, the angles marked as 120° are congruent, and the angles marked as 30° are congruent.
Next, let's compare the corresponding sides. In AABC, the side opposite the angle marked as 120° is 5 cm, and the side opposite the angle marked as 30° is (3x - 1) cm. In APQR, the side opposite the angle marked as 120° is 5 cm, and the side opposite the angle marked as 30° is (x + 5) cm.
Since the corresponding angles and sides in AABC and APQR are congruent, we can conclude that AABC is equal to APQR.
Now, let's find the lengths of AC and PR.
In AABC, AC is the side opposite the angle marked as 30°, which is (3x - 1) cm.
In APQR, PR is the side opposite the angle marked as 30°, which is (x + 5) cm.
Therefore, the lengths of AC and PR are (3x - 1) cm and (x + 5) cm, respectively.