Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q4.

Expert-verified

Geometry

Found in: Page 583

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Prove that you can see all of yourself in a mirror that is only half as tall as you are. (Hint: Study the diagram on page 582.)

It is proved that you can see all of yourself in a mirror that is only half as tall as you are.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The given statement is you can see all of yourself in a mirror that is only half as tall as you are.

Step 2. Proof.

Consider you are standing in front of a mirror of height FH and your height is AE.

Point C represents your eye, A represents top of your head, E represents foot, B is the mid-point between your eye and top of your head, D is the mid-point between your eye and foot, F is the bottom of the mirror, H is the top of the mirror and G is a point in the mirror parallel to your eyes.

Since,

$\begin{array}{l} A E = A B + B C + C D + D E \\ A E = B C + B C + C D + C D [A B = B C, C D = D E] \\ A E = 2 (B C + C D) (i) \\ and \\ H F = H G + G F (i i) \end{array}$

In similar triangles CGF and CDF

$\begin{array}{l} C F is common side \\ C D = D F \\ therefore, C D = G F \end{array}$

In similar triangles BCH and CGH

$\begin{array}{l} C H is common side \\ B H = C G \\ therefore, B C = H G \end{array}$

Substitute the values of HG and GF in equation i.

$\begin{array}{l} H F = H G + G F (i i) \\ H F = B C + C D [C D = G F, B C = H G] \\ H F = \frac{A E}{2} [A E = 2 (B C + C D)] \end{array}$

Step 3. Conclusion.

It is proved that you can see all of yourself in a mirror that is only half as tall as you are.

Most popular questions for Math Textbooks

Points A-D are reflected in the x-axis. Points E-H are reflected in the y-axis. State the coordinates of the images.

Complete the following. Assume points D, C, U, W, X, and Y are obtained by reflection in link k or j.

$R_{k} : \vec{B C} \to \underline{?}$

Complete the following. Assume points D, C, U, W, X, and Y are obtained by reflection in link k or j.

$R_{j} (\underline{?}) = \vec{X Y}$

Write the coordinates of the image of each point by reflection in,

The $x - a x i s$
The $y - a x i s$
The line $y = x$ (Hint: Refer to the Example on page 578)

Point A.

Complete the following. Assume points D, C, U, W, X, and Y are obtained by reflection in link k or j.

$R_{k} : A \to$ $\underline{?}$ .

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free