Question

Match the reasons with the statements in the proof to prove PT < PR given that PT is perpendicular to RT

Answer 1

$\overline{PT}\perp\overleftrightarrow{RT}$ is provided, so statement 1 pairs with the reason "Given".

Since perpendicular lines, by definition, form right angles where they meet, and ∠T is one of those meeting angles, we can match statement 2 with the 4th reason on the list, "Perpendicular lines form right angles"

In any right triangle, the two angles apart from the right angle must add to 90° which, except in the case where one of those angles is 0°, means that both must measure less than 90°. Since ∠R is one of those acute angles, we can say that m∠T > m∠R, so we can match statement 3 with reason 2, "The measure of a right angle is greater than the measure of an acute angle."

All triangles have the property that, given two interior angles, one bigger than the other, the side opposite the bigger angle will be bigger than the side opposite the smaller one. With this knowledge, we notice that since m∠T > m∠R, the side across from ∠T, $\overline{PR}$, must be bigger than the side across from ∠R, $\overline{PT}$. We can then match statement 4 with reason 1, which says the same thing.

Answer 2

Answer:

1.  

4

Perpendicular lines form right angles.  

2. T is a right angle  

2

The measure of a right angle is greater than the measure of an acute angle.  

3. m T > m R  

3

If two angles of a triangle are not equal, then the side opposite the larger angle is longer than the side opposite the smaller angle.  

4. PT < PR  

1

Given  

Step-by-step explanation: