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State whether the following statement is true or false.
Let AB is a line segment and P is its mid-point. If D and E are points on the same side of AB such that $∠ B A D = ∠ A B E and ∠ E P A = ∠ D P B$ (see figure), then

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True

False

answer is A.

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Detailed Solution

Given that,
In the figure, P is the midpoint of AB and

∠ B A D = ∠ A B E and ∠ E P A = ∠ D P A .

We have,

Adding

∠ E P D

on both sides of above equation, we get,

Since P is the mid-point of the line segment AB, then

∠ B A D = ∠ A B E

Thus, by ASA congruence rule:

Therefore, the given statement is true.
So, option (1) is correct.

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