Question

7
Show
that
the diagonals
of
a
rectangle
are
equal.​

Answer 1

Question:To show diagonals of a rectangle are equal

Given:

A rectangle ABCD in which AC and BD are the diagonals

To prove:

AC=BD

Proof:-

In ∆ABD and ∆BAC,we have

AB=BA (Common)

<A=<B (Each angle 90°)

AD=BC (Opposite sides of a llgm)

Therefore

∆ABC~∆BAC {S.A.S-criteria}

Hence, BD=AC

Answer 2

Step-by-step explanation:

Let ABCD be a rectangle

BD and AC are diagonals.

In triangles ABC and BCD,

Angle b =angle c (90 each)

AB = CD (opp. Sides of rectangle)

BC = BC (common)

By SAS.,triangles are congruent,

So AC=BD (CPCT)

Hence proved......