a Let's take a look at the given diagram presenting parallelogram PQRS that is one of several that change shape as the mirror is extended.
We are asked to determine what happens to m∠ P as m∠ Q increases.
Let's recall that the sum of the consecutive angles in a parallelogram are supplementary meaning their sum is constantly equal to 180^(∘). This means that when m∠ Q increases m∠ P must decrease.
b Again, let's start with taking a look at the given diagram presenting parallelogram PQRS that is one of several that change shape as the mirror is extended.
This time we are asked to determine what happens to QS as m∠ Q decreases.
Let's recall that the sum of the consecutive angles in a parallelogram are supplementary meaning their sum is constantly equal to 180^(∘). This means that when m∠ Q decreases m∠ P must increase.
Notice that QS is a side of a △ PQS that is opposite to ∠ P. Therefore, according to the Hinge Theorem, when m∠ P increases, QS must also increase.
c Finally, let's take a look at the given diagram presenting parallelogram PQRS that is one of several that change shape as the mirror is extended.
Now, we are asked to determine what happens to the overall distance between the mirror and the wall when m∠ Q decreases. This means that we should analyze what happens to PR.
Let's notice that PR is a side of a △ PQR that is opposite to ∠ Q. Therefore, according to the Hinge Theorem, when m∠ Q decreases PR must also decrease. This means that the overall distance between the mirror and the wall decreases as m∠ Q decrease.
