Question

In the diagram below, TUVW is a rectangle. Prove triangle TZW is congruent to triangle UZV.

Answer 1

By S.S.S. congruence property; ΔTZW ≅ ΔVZU

Explanation:

Given:

TUVW is a rectangle.

To Prove : TZW ≅ UZV

Proof:

Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.

So,

`TW = UV \ \ .\ .\ .\ .\ 1`

And also TV and WU are the diagonals of the rectangle.

And the diagonals of rectangle bisects each other.

Therefore;

`TZ=ZV.........\ 2\\\\WZ=ZU..........\ 3`

Now In ΔTZW and ΔVZU

TW = UV (from 1)

TZ = ZV (from 2)

WZ = ZU (from 3)

So, by S.S.S. congruence property;

ΔTZW ≅ ΔVZU

Hence proved.