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1.) Prove that PAT is an isosceles triangle.
2.) State The Coordinates of R so that quadrilateral PART is a parallelogram.

( The image of the Question Is Given )

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1 Prove that PAT is an isosceles triangle 2 State The Coordinates of R so that quadrilateral PART is a parallelogram The image of the Question Is Given First on class=

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MrRoyal

The triangle PAT is an isosceles triangle because the side lengths PA and AT are congruent

How to prove that the triangle is an isosceles triangle?

The points are given as:

P = (1,6)

A = (4,5)

T = (5,2)

Calculate the distance between both points as follows:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]PA = \sqrt{(1 -4)^2 + (6-5)^2}[/tex]

[tex]PA = \sqrt{10}[/tex]

[tex]PT = \sqrt{(1 -5)^2 + (6-2)^2}[/tex]

[tex]PT = \sqrt{32}[/tex]

[tex]AT = \sqrt{(4 -5)^2 + (5-2)^2}[/tex]

[tex]AT = \sqrt{10}[/tex]

Because the side lengths PA and AT are congruent, i.e. √10, then the triangle is an isosceles triangle

Read more about isosceles triangle at:

https://brainly.com/question/1475130

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