Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 5: Q3 (page 192)

For the following figure, $X, Y, Z$ are the midpoints of the sides of isosceles $螖 A B C$ . Name an isosceles trapezoid and find its perimeter.

Short Answer

Expert verified

The trapezoid is $C X Y B$ and the perimeter is 22.

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

The isosceles trapezoid is a quadrilateral with one pair of parallel lines and one pair of

sides are of equal length.

Consider the triangle $螖 A B C$ .

Here the points $X, Y$ and $Z$ are the midpoints of $\overset{炉}{A C}, \overset{炉}{A B}$ and $\overset{炉}{B C}$

Now,

$\begin{array}{l} \overset{炉}{C X} = \frac{A C}{2} = \frac{10}{2} = 5 \\ \overset{炉}{B Y} = \frac{A B}{2} = \frac{10}{2} = 5 \\ \overset{炉}{Z B} = \frac{B C}{2} = \frac{8}{2} = 4 \\ \overset{炉}{C X} = \overset{炉}{B Y} = 5 (1) \end{array}$

Thus, $X Y Z B$ is a parallelogram so the opposite sides are equal.

$\begin{array}{l} X Y | | Z B | | C B \\ X Y | | C B \\ X Y = Z B = 4 (2) \end{array}$

Step 3. Step description.

Now, $C X Y B$ has one pair of parallel lines and one pair of equal sides.

So $C X Y B$ is the isosceles trapezoid.

Calculate the perimeter of $C X Y B$ as follows:

$\begin{array}{l} = C X + X Y + B Y + B C \\ = 5 + 4 + 5 + 8 \\ = 22 \end{array}$

Therefore, the perimeter of the trapezoid $C X Y B$ is 22 units.

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91影视

For the following figure, $X, Y, Z$ are the midpoints of the sides of isosceles $螖 A B C$ . Name an isosceles trapezoid and find its perimeter.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

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91影视

For the following figure, X,Y,Zare the midpoints of the sides of isosceles 螖ABC. Name an isosceles trapezoid and find its perimeter.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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For the following figure, $X, Y, Z$ are the midpoints of the sides of isosceles $螖 A B C$ . Name an isosceles trapezoid and find its perimeter.