Mastering Parallelograms: Answer Key for Unit 7 Polygons and Quadrilaterals Homework 2

# Introduction

In this unit, we will delve into the fascinating world of polygons and quadrilaterals. One specific type of quadrilateral that we will explore is the parallelogram. In this article, we will provide an answer key for Unit 7 Polygons and Quadrilaterals Homework 2, which focuses on mastering the concepts related to parallelograms.

## Properties of Parallelograms

Before we dive into the answer key, let’s have a quick overview of the properties of parallelograms. A parallelogram is a quadrilateral with two pairs of parallel sides. Here are some important properties:

**Opposite sides:**The opposite sides of a parallelogram are congruent. In other words, they have the same length.**Opposite angles:**The opposite angles of a parallelogram are congruent. This means they have equal measures.**Consecutive angles:**The consecutive angles (adjacent angles sharing one side) in a parallelogram add up to 180 degrees.**Diagonals:**The diagonals of a parallelogram bisect each other. This means that they divide each other into two equal parts.

## Solving Homework Problems

### Hints for Problem 1: Finding Missing Side Lengths

In problem 1, you are given a partial information about a parallelogram and asked to find missing side lengths. To approach this problem:

- Start by labeling the given side lengths and angles.
- Use the properties of parallelograms to identify any congruent or supplementary angles.
- Apply appropriate geometric theorems and formulas to find the missing side lengths.

### Hints for Problem 2: Calculating Area

Problem 2 requires you to calculate the area of a parallelogram. Follow these steps:

- Identify the base and the height of the parallelogram.
- Multiply the base by the height to find the area. Remember, both measurements should be in the same units.

### Hints for Problem 3: Determining Congruence

In problem 3, you are given two parallelograms and asked to determine if they are congruent. To do so:

- Note down all given information about each parallelogram, such as side lengths, angles, and diagonals.
- Check if all corresponding sides are congruent and if all corresponding angles have equal measures.
- If all corresponding parts are equal, you can conclude that the two parallelograms are congruent.

## Conclusion

Congratulations on completing Unit 7 Polygons and Quadrilaterals Homework 2! By mastering these problems related to parallelograms, you have gained a deeper understanding of their properties and how to solve various types of questions involving them. Don’t forget to practice further on your own to solidify your knowledge!