Mathematics, 13.07.2019 22:00, mochoa4

Match the reasons with the statements in the proof to prove pt < pr given that pt is perpendicular to rt

Match the reasons with the statements in the proof to prove pt < pr given that pt is perpendicul

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answered: serenityjohnson98765

Option 1 matches the reason 3.Option 2 matches the reason 4.Option 3 matches the reason 2.Option 4 matches the reason 1.

Given-

The length PT is perpendicular to the length RT.

Option 1) $\overline {PT}$ perpendicular to the $\overline {RT}$ -The above equation indicate that the length PT is perpendicular to the length RT. This statement is already given in the problem given. Thus the option 1 matches to the Reason 3.Option 2- $\angle T$ is the right angle-The angle which is of exactly 90 degrees is called right angle. According to the perpendicular lines theorem when two lines are perpendicular they do intersect, and they intersect at right angle. Thus the perpendicular lines form right angle. Therefore the option 2 matches the reason 4.Option 3- $m\angle Tm\angle R$ - $\angle T$ is actuate angle and $\angle R$ is right angle. Actuate angle measures less then 90 degrees and the measures of right angle is equal to the 90 degrees. Thus the measure of right angle is greater than the measures of actuate angle. Hence the option 3 matches the reason 2.Option 4- $\overline {PT}< \overline {RT}$ -According to the converse of longer side inequality theorem "If two angles of a triangle are not equal then side of opposite the larger angle is greater than the side opposite the smaller angle". Here side RT is the side of opposite the larger angle and side PT is the side opposite the smaller angle in the given question. Thus the option 4 matches the reason 1.

Hence,

Option 1 matches the reason 3.

Option 2 matches the reason 4.

Option 3 matches the reason 2.

Option 4 matches the reason 1.

For more about the right angle triangle, follow the link below

link?

answered: whitakers87

$\overline{PT}\perp\overleftrightarrow{RT}$ 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.