Question

D 14. In the given figure, ABCD is a square and P is a point inside it such that PB = PD. Prove that CPA is a straight line. P А B​

Answer 1

Answer:

It is given that is a square and is a point inside it such that

Considering and

We know that all the sides are equal in a square

So we get

is common i.e.

According to congruence criterion

We get

Considering and

We know that all the sides are equal in a square

So we get

is common i.e.

According to congruence criterion

We get

By adding both the equation (1) and (2)

From the figure we know that the angles surrounding the point is

So we get

By grouping we get

Now by substitution of (4) in (3)

On further calculation

By division we get

Therefore, it is proved that is a straight line.

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