# Lesson 4 Prove It Right Practice Understanding

## Learning Focus

Prove quadrilaterals are parallelograms, rectangles, rhombi, or squares using coordinates.

Find the perimeter and area of a quadrilateral on the coordinate plane.

How do I use algebra to show that a quadrilateral is a parallelogram, a rectangle, a rhombus, or a square?

## Open Up the Math: Launch, Explore, Discuss

In this lesson you need to use all the things you know about quadrilaterals, distance, and slope to prove that the shapes are parallelograms, rectangles, rhombi, or squares. Be systematic and be sure that you give all the evidence necessary to verify your claim.

### 1.

#### a.

Is

#### b.

Is

### 2.

#### a.

Is

#### b.

Is

#### c.

Find the perimeter of each of the figures in the diagram.

### 3.

#### a.

Is

#### b.

Is

#### c.

Find the area of each of the figures in the diagram.

### 4.

#### a.

Find the midpoint of side

#### b.

Now find the point

#### c.

Find the area of triangle

## Ready for More?

Find the midpoints of each of the sides of quadrilateral

## Takeaways

Ways to use coordinates to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares:

## Lesson Summary

In this lesson, we used the distance formula, the midpoint rule, and the properties of slopes of parallel and perpendicular lines to determine if a given set of

### 1.

Find the value of

### 2.

Find the perimeter for the triangle and the semicircle on the grid.