# LINR 3 | Lesson 4 | Making Connections Solutions

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 $$AB^2 + BC^2= AC^2$$.

1. 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 $$-\dfrac{1}{4}$$. 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.