We want to fill in the blanks of the given statement.
If QP≅QR, then ∠ ≅ ∠ .
The first part of the statement, QP≅ QR, tells us that these two sides are congruent. Let's mark this in our diagram.
We want to find the congruent angles, given that segments QP and QR are congruent. To do so, we will use the Base Angles Theorem. Let's recall that theorem.
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
By this theorem, since we know that two sides of the triangle — QP and QR — are congruent, then we also know that the angles opposite them are congruent. Let's show this in our diagram.
Based on the diagram and the theorem, we know that the marked angles are congruent. Now we can complete the statement.
