# In Fig. 6.16, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD

**Solution:**

Given, in triangles ABP and CPD ∠A = ∠C.

The lengths of

AB = 6 cm

BP = 15 cm

AP = 12 cm

CP = 4 cm

We have to find the lengths of PD and CD.

In △ABP and △CDP,

Given, ∠A = ∠C

So, ∠BAP = ∠PCD

Vertically opposite angles are equal

∠BPA = ∠CPD

AAA criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.

By AAA criterion, △ABP ⩬ △CDP.

By the property of similarity,

The corresponding sides are in proportion.

AB/DC = BP/PD = AP/CP

6/DC = 15/PD = 12/4

6/DC = 15/PD = 3

Considering 6/DC = 3

3DC = 6

DC = 6/3

DC = 2 cm

Considering 15/PD = 3

3PD = 15

PD = 15/3

PD = 5 cm

Therefore, the length of PD and CD are 5 cm and 2 cm respectively.

**✦ Try This:** In given figure, ABC is a triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then find BD and AB.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 6

**NCERT Exemplar Class 10 Maths Exercise 6.4 Problem 1**

## In Fig. 6.16, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD

**Summary:**

In Fig. 6.16, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then the lengths of PD and CD are 5 cm and 2 cm respectively

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