## Unit 7 Polygons and Quadrilaterals Homework 7 Trapezoids Answer Key

### Introduction

Unit 7 of the Polygons and Quadrilaterals curriculum focuses on trapezoids, a unique type of quadrilateral with distinct properties. In this article, we will provide the answer key for Homework 7, which covers various aspects of trapezoids. By understanding the correct answers, you will be able to enhance your understanding of trapezoids and apply your knowledge to solve problems effectively. Let's dive into the answer key and explore the world of trapezoids!

### Question 1: Definition of a Trapezoid

The first question in Homework 7 asks you to define a trapezoid. A trapezoid is a quadrilateral with at least one pair of parallel sides. This definition is crucial to differentiate trapezoids from other quadrilaterals, such as rectangles or squares, which have all their sides parallel.

### Question 2: Identifying Trapezoids

In this question, you are given a set of figures and asked to identify which ones are trapezoids. To solve this, you need to examine the shapes and check if they meet the definition of a trapezoid. Remember, at least one pair of sides must be parallel. By carefully analyzing the figures, you will be able to determine the trapezoids correctly.

### Question 3: Properties of Trapezoids

This question focuses on the properties of trapezoids. You are asked to identify the true statements about trapezoids from a given list. To solve this, you need to recall the properties of trapezoids, such as the base angles being supplementary and the diagonals dividing each other proportionally. By understanding these properties, you can identify the correct statements and eliminate the false ones.

### Question 4: Calculating the Area of a Trapezoid

In this question, you are provided with the dimensions of a trapezoid and asked to find its area. To calculate the area of a trapezoid, you need to use the formula: Area = (1/2) * (sum of bases) * height. By plugging in the given values into the formula and performing the necessary calculations, you will be able to determine the correct answer.

### Question 5: Finding the Missing Side Lengths

This question challenges you to find the missing side lengths of a trapezoid. You are given the lengths of the bases and one of the legs, and you need to calculate the lengths of the remaining sides. To solve this, you can utilize the properties of trapezoids, such as the opposite sides being congruent. By setting up equations and solving for the missing side lengths, you will arrive at the correct answers.

### Question 6: Classifying Trapezoids

In this question, you are presented with different trapezoids and asked to classify them based on their properties. To classify a trapezoid, you need to examine its angles and sides. For example, if a trapezoid has congruent legs, it is called an isosceles trapezoid. By analyzing the given trapezoids and applying your knowledge of trapezoid classifications, you will be able to correctly classify them.

### Question 7: Constructing Trapezoids

This question involves constructing trapezoids based on given specifications. You are provided with certain side lengths and angles, and you need to use a compass and straightedge to construct the trapezoids. By following the steps of construction and utilizing your geometric skills, you will be able to construct trapezoids that meet the given requirements.

### Question 8: Real-life Examples of Trapezoids

In this question, you are asked to identify real-life examples of trapezoids. Trapezoids can be found in various objects and structures, such as rooftops, road signs, or tables. By observing your surroundings and recognizing the shapes of trapezoids, you will be able to identify the correct examples.

### Question 9: Applying Trapezoid Properties

This question requires you to apply the properties of trapezoids to solve a problem. You are presented with a scenario and asked to find a specific measurement or angle. By utilizing your knowledge of trapezoid properties, such as the sum of interior angles being 360 degrees, you will be able to solve the problem effectively.

### Question 10: Generalizing Trapezoid Properties

In the final question, you are asked to generalize the properties of trapezoids. This involves reflecting on the various properties you have learned throughout the unit and identifying the common characteristics of trapezoids. By summarizing these properties and expressing them in a generalized form, you will demonstrate a deep understanding of trapezoids.

### Conclusion

By going through the answer key for Homework 7 on trapezoids, you have gained a comprehensive understanding of this unique type of quadrilateral. From understanding the definition of a trapezoid to applying its properties in problem-solving, you have developed a solid foundation in trapezoid geometry. Keep practicing and exploring the world of polygons and quadrilaterals to further enhance your mathematical skills!