Question

Prove that the diagonals of a cyclic parallelogram are equal.​

Answer 1

Solution:

Given: ABCD is a cyclic quadrilateral in which AD and BC are equal  RTP:

AC = BD

Construction:Join AC and BD.

Proof: From  ΔADC and ΔBDC, We know that same segments subtends equal angles on the circumference of a circle So, ∠CAD = ∠CBD We know that equal lengths of chords  subtends equal angles on  the circumference of a circle So,

∠ACD = ∠BDC And  AD= BC       

 Given ⇒ Δ ADC ≅ Δ BCD  By AAS congruence rule  

AC = BD         [By CPCT]

Hence proved  

Answer 2

Answer:

Step-by-step explanation:

Given: ABCD is a cyclic quadrilateral in which AD and BC are equal  

RTP: AC = BD

Construction: Join AC and BD.

Proof:

From  ΔADC and ΔBDC,

We know that same segments subtends equal angles on the circumference of a circle

So, ∠CAD = ∠CBD

We know that equal lengths of chords  subtends equal angles on  the circumference of a circle

So, ∠ACD = ∠BDC

And  AD= BC         [∵Given]

⇒ Δ ADC ≅ Δ BCD     [∵ By AAS congruence ru;le]

∴  AC = BD         [By CPCT]

Hence proved