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

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)   perpendicular to the -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- 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-- is actuate angle and 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--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.

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