Question

GIVEN:


AC = 6 cm, AB = 12 cm, BC = 15 cm


CE = 8 cm, CD = 20 cm, ED = 16 cm


PROVE:


Angle B is congruent to Angle D

Answer 1

Answer:

Given: ∠A=∠C,AB=6cm,BP=15cm,AP=12cm CP=4

To fine. lengths of PD and CD

Sol. In ΔABP and ΔCDP,

∠A=∠C (Given)

∠2=∠1 (Vertically opposite angles)

∴ΔABP∼ΔCDP [By AA similarity criterion]

Refer image.

=

CD

AB

=

CP

AP

=

DP

BP

(since corresponding sides of two similar triangles are proportional)

=

y

6

=

4

12

=

x

15

=

y

6

=

4

12

=y=

12

6×4

=2cm

=

x

15

=

4

12

⇒

x

15

=3

⇒x=5cm

∴PD=5cm AND CD=2cm

Answer 2

PD = 5cm

and CD= 2cm

hope it helps