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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