### Home > CC3MN > Chapter 9 > Lesson 9.2.1 > Problem9-108

9-108.

Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral $ABCD$ on a coordinate grid with $A(1, 4)$, $B(6, 6)$, $C(4, 1)$, and $D(–1, –1)$.

1. A rhombus has four sides that are equal length. Is $ABCD$ a rhombus? Show how you know.

Create slope triangles on each side. Visualize them using the eTool, then draw them on your paper.

Use the Pythagorean Theorem to calculate the length of each side. Are they the same? If so, the shape is a rhombus.

2. Write the equations of the lines on which the diagonals lie. That is, write the equations of $\overleftrightarrow{ A C }$and $\overleftrightarrow{ B D }$.

Connect points $A$ and $C$ and points $B$ and $D$. Use slope-intercept form ($y = mx + b$) to write the equations of the lines. Test your equations in the eTool to be sure they are correct.

3. Compare the slopes of $\overleftrightarrow{ A C }$ and $\overleftrightarrow{ B D }$. What do you notice?

What is true about the slopes of parallel and perpendicular lines?

Use the eTool below for help with parts (a-c).
Click the link at right for the full version of the eTool: 9-108 HW eTool