ICSE Class 10CISCE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

In a Cyclic-trapezium, the Non-parallel Sides Are Equal and the Diagonals Are Also Equal. Prove It. - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal. Prove it.

Solution


A cyclic trapezium ABCD in which AB ∥ DC and AC and BD are joined.
To prove-
(i) AD = BC
(ii) AC = BD
Proof :
∵ chord AD subtends ∠ABD and chord BC subtends BDC
At the circumference of the circle.

But ∠ABD = ∠BDC   [proved]
Chord AD = Chord BC
⇒ AD = BC    

Now in ∆ADC and ∆ BCD

DC = DC      [Common]

∠CAD = ∠CBD           [angles in the same segment]

And  AD = BC        [proved]

By Side – Angle – Side criterion of congruence, we have

∴ ∆ADC ≅ ∆BCD       [ SAS axion]

The corresponding parts of the congruent triangle are congruent

 ∴ AC = BD       [c.p.c.t]

  Is there an error in this question or solution?
Solution In a Cyclic-trapezium, the Non-parallel Sides Are Equal and the Diagonals Are Also Equal. Prove It. Concept: Arc and Chord Properties - Angles in the Same Segment of a Circle Are Equal (Without Proof).
S
View in app×