Question

In the given figure AB | DE and BC=CD. Given AB = 2x - 4, AC = 3y + 5,
DE-14 cm and CE-20cm​.
1) Prove triangle ABC is corresponding to triangle EDC
2) Find the value of x and y​

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

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