Question

9. ABCD is a parallelogram. If the two diagonals are equal, find the measure of LABC.
10. In AABC and AADC, AB = AD and BC = CD. Prove that ZABC AADC.
11. Prove that angles opposite to equal sides of an isosceles triangle are equal.​

Answer 1

Step-by-step explanation:

9.In a parallelogram if two diagonals are equal, then the parallelogram is a rectangle.So, ABCD is a rectangle.It is known that each interior angle of a rectangle is 90 degree.Since ABC is an interior angle of rectangle ABCD, so measure of angle ABC is 90 degree.

10.Given : AB=AD

: CB=CD

To prove :ABC is congruent to ADC

Proof :

In triangle ABC and ADC,

AB=AD AND CD=CB (Given)

AC=AC (Common)

So, according to SSS congruency rule,

ABC is congruent to ADC

Hence proved..

11.Take a triangle ABC, in which AB=AC.

Construct AP bisector of angle A meeting BC at P.

In ∆ABP and ∆ACP

AP=AP[common]

AB=AC[given]

angle BAP=angle CAP[by construction]

Therefore, ∆ABP congurent ∆ACP[S.A.S]

This implies, angle ABP=angleACP[C.P.C.T]

Hence proved that angles opposite to equal sides of a triangle are equal.

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Answer 2

Answer:

I have no answer . ok Bye Bye