# ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ

**Solution:**

Given: ABCD is a parallelogram and AP ⊥ DB, CQ ⊥ DB

**(i)** In ΔAPB and ΔCQD,

∠APB = ∠CQD (Each 90°)

AB = CD (Opposite sides of parallelogram ABCD)

∠ABP = ∠CDQ (Alternate interior angles as AB || CD)

∴ ΔAPB ≅ ΔCQD (By AAS congruency)

**(ii)** By using the result ΔAPB ≅ ΔCQD., we obtain AP = CQ (By CPCT)

**Video Solution:**

## ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ

### NCERT Maths Solutions Class 9 - Chapter 8 Exercise 8.1 Question 10:

**Summary:**

If ABCD is a parallelogram where AP and CQ are perpendiculars from vertices A and C on BD, then ΔAPB ≅ ΔCQD using AAS congruency and AP = CQ.