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