### Video Transcript

In the given figure, points πΏ
and π are on a circle with center π. Which congruence criterion can
be used to prove that triangles ππΏπ and πππ are congruent?

In this problem, we need to
determine how we can prove that these two triangles ππΏπ and πππ are
congruent, which means that corresponding sides are congruent and corresponding
angles are congruent. We might notice that both of
these triangles have a right angle. And there is a congruency
criterion which applies in right triangles. It is the RHS criterion, which
tells us that two triangles are congruent if they have a right angle and the
hypotenuse and one other side are equal.

Letβs see if we can apply this
criterion here. And even though we arenβt given
any length measurements, we can apply our knowledge of geometry to help. Because weβre given that πΏ and
π are on the circle and the center is π, then the line segments ππΏ and ππ
are both radii of the circle. And importantly, that means
that these are congruent. We also have this line segment
ππ, which is a shared side between the two triangles. So this length will be equal in
both triangles. Very helpfully, we can also
recognize that the line segment ππ is the hypotenuse in both of these
triangles.

Now, if we look at the RHS
criterion, we know that both triangles do have a right angle. We also know that the
hypotenuse is congruent because this is a common side. And we have another pair of
sides which are congruent. Therefore, it is by applying
the RHS congruence criterion that we can prove that triangles ππΏπ and πππ
are congruent.