ICSE Class 10CISCE
Share
Notifications

View all notifications

In the Following Figure Ab = Ac. Prove that Decb is an Isosceles Trapezium. - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

In the following figure AB = AC. Prove that DECB is an isosceles trapezium.

Solution


Here, AB = AC
⇒ ∠B =∠C
∴ DECB is a cyclic quadrilateral
(Ina triangle, angles opposite to equal sides are equal)
Also, ∠B + ∠DEC = 180°   ………. (1)
(pair of opposite angles in a cyclic quadrilateral are supplementary)
⇒∠C + ∠DEC = 180°  [from (1)]

But this is the sum of interior angles

On one side of a transversal.

∴ DE || BC But  ∠ADE = ∠AED = ∠C [Corresponding angles]

Thus, ∠ADE = ∠AED
⇒AD = AE
⇒ AB - AD = AC - AE( ∴ AB = AC)
⇒ BD = CE
Thus, we have, DE || BC and BD = CE
Hence, DECB is an isosceles trapezium

  Is there an error in this question or solution?
Solution In the Following Figure Ab = Ac. Prove that Decb is an Isosceles Trapezium. Concept: Cyclic Properties.
S
View in app×