Question

in the given figure AB||DE and BC=CD, given 2x-4,Ac=3y+5,DE=14 and Ce= 20cm

​

Answer 1

Given : AB || DE and BC = CD

AB = 2x - 4.AC = 3y + 5,

DE = 14 cm and CE = 20 cm

To Find :  1) Prove triangle ABC is congruent to triangle EDC

2) Find the value of x and y​

Solution:

AB || DE and BD transversal

=> ∠DBA = ∠BDE  ( alternate angles)

C lies on BD

=> ∠CBA = ∠CDE

ΔABC  and ΔEDC

∠BCA = ∠DCE  ( Vertically opposite angles)

BC  = CD   Given

∠CBA = ∠CDE  (shown above)

=> ΔABC  ≅  ΔEDC  (ASA)

AB = DE     CPCT

AC = CE     CPCT

AB = DE     => 2x - 4  = 14  => x = 9

AC = CE     => 3y + 5 = 20 => y = 5

ΔABC  ≅  ΔEDC

Value of x = 9 and value of y = 5

Learn More:

In the given figure AB || DE and BC = CD.

https://brainly.in/question/34361208

In triangle LMN and triangle OPN, if triangle LMN = triangle NPO ...

brainly.in/question/14439006

Given two congruent triangles prove that the bisectors of one ...

brainly.in/question/12071246