# Understanding Unit 10 Circles Homework 4: Congruent Chords & Arcs

The fourth homework assignment in Unit 10 Circles focuses on congruent chords and arcs. It is important to have a good understanding of congruent chords and arcs in order to complete the assignment successfully. This article will provide an overview of what congruent chords and arcs are and how to use them in your homework. Read on to learn more!

## What are Congruent Chords and Arcs?

Congruent chords and arcs are two circles with the same radius, or two arcs of equal length. They are said to be congruent when they are exactly the same size and shape. For example, if two circles have the same diameter, or two arcs have the same central angle, then they are congruent. Congruent chords and arcs can be used to make calculations in geometry and can also be used to solve many problems.

## How to Use Congruent Chords and Arcs in Unit 10 Circles Homework 4

In Unit 10 Circles homework 4, you will be asked to use congruent chords and arcs to find measures of angles, lengths of arcs, and areas of circles. To find the measures of angles, you must use the theorem of congruent chords, which states that the measure of an angle formed by two congruent chords is equal to one-half the sum of the measures of the arcs intercepted by the chords. To find the length of an arc, you must use the theorem of congruent arcs, which states that if two arcs are congruent, then their lengths are also equal.

## Example Problem

Let’s look at an example problem to further understand how to use congruent chords and arcs in Unit 10 Circles homework 4. Suppose you are given two circles, one with a radius of 5 cm and the other with a radius of 10 cm. You are asked to find the measure of the arc intercepted by two congruent chords. To solve this problem, you must first use the theorem of congruent chords to find the measure of the angle formed by the two congruent chords. This angle is equal to one-half the sum of the measures of the arcs intercepted by the chords. Since the two circles have the same radius, the measure of the arcs intercepted by the chords is equal to 180 degrees. Therefore, the measure of the angle formed by the two congruent chords is equal to 90 degrees.

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In conclusion, congruent chords and arcs can be used to solve many problems in Unit 10 Circles homework 4. By understanding what congruent chords and arcs are and how to use them, you can successfully complete the fourth homework assignment in Unit 10 Circles. Hopefully, this article has helped you better understand congruent chords and arcs and how to use them in your homework.