Question

help me please only if you’re good with geometry. i’ve asked multiple tutors and no one can do it. i need this done in a two column flow chart.

Answer 1

As per given by the question,

There are given that a quadrilaterals.

Now,

There are also given that ,

$\begin{gathered} \angle P=\angle S \\ m\angle P+m\angle Q=180^{\circ} \\ m\angle R+m\angle S=180^{\circ} \\ PS\cong QR \end{gathered}$

Then,

From the properties of the rectangle;

First: the sum of its internal angles is 360 degree,

That means, all the angle of a rectangle are 90 degree.

Second: Opposite sides of a rectangle are equal and parallel.

Third: Diagonals of a rectangle bisects each other.

Now,

From the given properties;

Now,

According to the given properties,

The given figure PQRS is a rectangle.

That means,

All angles are 90 degree,

So;

$\angle P=\angle Q=\angle S=\angle R=90^{\circ}$

Then,

Sum of any two angle is 190 degree.

And,

The opposite sides of the rectangle are equal and parallel.

Hence, PQRS is a rectangle.