1. Vertices are: A: \((-2,2)\), B:\((0,0)\) , and C: \( (2,2)\).

Segment AB: \(m = -1\); segment BC: \(m = 1\); since the slopes are negative reciprocals the lines containing the segments are perpendicular so ∠ABC is a right angle.

If you remember the Pythagorean theorem and the Distance Formula you can also prove that \(AB^2 + BC^2= AC^2\).

2. Vertices are A: \((1,1)\), B:\((2, 5)\), C: \((6,4)\) and D:\((5,0)\)

Slopes of the sides AB and CD are 4 and slopes of sides AD and BC are \(-\frac{1}{4}\). Therefore AB||CD and AD||BC and ABCD is a parallelogram by definition, Also AB is perpendicular to AD. The quadrilateral is a rectangle.

You can also show by using the Distance Formula that a pair of opposite sides are congruent and parallel.

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