Explanation Given: The figure is given by, Redraw the given figure and mark on the mirror m a point P other than M as shown below in Figure 1. Because the angle of incidence is congruent to the angle of reflection, the respective complements of these angles must be congruent and α = β . Here, B ′ is the image of B under the reflection in m and hence ∠ P M B ′ is the image of ∠ P M B . Notice that β , the measure of ∠ P M B , must equal β 1 , the measure of ∠ P M B ′ , because reflection preserves angle measurement

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

12th Edition

ISBN: 9780321987297

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

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Chapter 13, Problem 8NT

To determine

To prove:

The inequality AM+MB<AP+PB and show that MB=MB′ and BP=B′P, and then use the Triangle Inequality applied to ΔAPB′, and that A, M, and B′ are collinear.

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Chapter 13, Problem 5NT

Chapter 14.1, Problem 2MC

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Chapter 13 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

Ch. 13.1 - Prob. 1MC Ch. 13.1 - Prob. 3MC Ch. 13.1 - When a line is rotated about a point O, by angle ,...Ch. 13.1 - Prob. 6MC Ch. 13.1 - Prob. 7MC Ch. 13.1 - Prob. 8MC Ch. 13.1 - A drawing of a cube, shown in the following...Ch. 13.1 - Wall stenciling has been used to obtain an effect...Ch. 13.1 - Prob. 11MC Ch. 13.1 - Prob. 12MC

Ch. 13.1 - Prob. 13MC Ch. 13.1 - Prob. 14MC Ch. 13.1 - Prob. 15MC Ch. 13.1 - Prob. 16MC Ch. 13.1 - Prob. 19MC Ch. 13.1 - Prob. 1NAEP Ch. 13.1A - For each of the following, find the image of the...Ch. 13.1A - Construct the image BC under the translation...Ch. 13.1A - Find the coordinates of the image for each of the...Ch. 13.1A - Prob. 4A Ch. 13.1A - Prob. 7A Ch. 13.1A - Prob. 8A Ch. 13.1A - If y=2x+3 is the image of the line k under the...Ch. 13.1A - Prob. 10A Ch. 13.1A - Prob. 11A Ch. 13.1A - Prob. 12A Ch. 13.1A - a. Draw a line l and any two points A and B so...Ch. 13.1A - Prob. 14A Ch. 13.1A - Prob. 15A Ch. 13.1A - Prob. 16A Ch. 13.1A - Prob. 18A Ch. 13.1A - a. Use a drawing similar to Figure 19 to find the...Ch. 13.1A - Prob. 20A Ch. 13.1A - Prob. 21A Ch. 13.1A - Prob. 22A Ch. 13.1A - Prob. 23A Ch. 13.1A - Prob. 24A Ch. 13.1A - Prob. 26A Ch. 13.1B - Prob. 2A Ch. 13.1B - Prob. 3A Ch. 13.1B - Prob. 4A Ch. 13.1B - Prob. 7A Ch. 13.1B - Prob. 8A Ch. 13.1B - Prob. 9A Ch. 13.1B - Prob. 11A Ch. 13.1B - Prob. 12A Ch. 13.1B - Prob. 13A Ch. 13.1B - Prob. 14A Ch. 13.1B - Prob. 15A Ch. 13.1B - Find the equation of the image of the line y=3x1...Ch. 13.1B - Prob. 20A Ch. 13.1B - Prob. 21A Ch. 13.1B - Prob. 22A Ch. 13.2 - Prob. 1MC Ch. 13.2 - Prob. 2MC Ch. 13.2 - Prob. 3MC Ch. 13.2 - Prob. 4MC Ch. 13.2 - Prob. 5MC Ch. 13.2 - Prob. 6MC Ch. 13.2 - Andrea, a civil engineer, was asked to make a plan...Ch. 13.2 - Prob. 8MC Ch. 13.2 - Prob. 9MC Ch. 13.2 - Prob. 10MC Ch. 13.2 - Prob. 11MC Ch. 13.2 - Gloria claims that Sammis example in problem 14 is...Ch. 13.2 - Prob. 18MC Ch. 13.2 - Prob. 19MC Ch. 13.2 - Prob. 20MC Ch. 13.2 - Prob. 22MC Ch. 13.2 - Prob. 1NAEP Ch. 13.2 - Prob. 2NAEP Ch. 13.2 - Prob. 3NAEP Ch. 13.2A - Assessment 14-2A Describe how to find the image of...Ch. 13.2A - Prob. 2A Ch. 13.2A - Assessment 14-2A Determine the final result when...Ch. 13.2A - Prob. 4A Ch. 13.2A - Assessment 14-2A a. Refer to the following figure...Ch. 13.2A - Prob. 6A Ch. 13.2A - Assessment 14-2A Given ABC and its reflection...Ch. 13.2A - a. The word TOT is its own image when it is...Ch. 13.2A - Find the equation of the image of the line with...Ch. 13.2A - Prob. 10A Ch. 13.2A - Decide whether a reflection, a translation, a...Ch. 13.2A - a. Conjecture what the image of a point with...Ch. 13.2A - Prob. 16A Ch. 13.2A - Prob. 17A Ch. 13.2A - Prob. 18A Ch. 13.2A - Point P is the image of P not shown under a glide...Ch. 13.2A - Consider the glide reflection determined by the...Ch. 13.2B - Prob. 1A Ch. 13.2B - Prob. 2A Ch. 13.2B - Determine the final result when ABCis reflection...Ch. 13.2B - Prob. 4A Ch. 13.2B - Prob. 6A Ch. 13.2B - Prob. 7A Ch. 13.2B - Prob. 8A Ch. 13.2B - Prob. 9A Ch. 13.2B - Prob. 10A Ch. 13.2B - Prob. 11A Ch. 13.2B - Prob. 12A Ch. 13.2B - Prob. 13A Ch. 13.2B - Prob. 14A Ch. 13.2B - Prob. 15A Ch. 13.2B - In which line will the two intersecting circles...Ch. 13.2B - Prob. 18A Ch. 13.2B - If PQ is the image PQ not shown under a glide...Ch. 13.2B - Prob. 20A Ch. 13.2B - Prob. 21A Ch. 13.3 - Prob. 1MC Ch. 13.3 - Prob. 2MC Ch. 13.3 - Prob. 3MC Ch. 13.3 - Prob. 5MC Ch. 13.3 - Prob. 6MC Ch. 13.3 - Prob. 7MC Ch. 13.3 - Prob. 8MC Ch. 13.3 - Prob. 9MC Ch. 13.3 - Prob. 10MC Ch. 13.3 - Prob. 11MC Ch. 13.3 - Prob. 12MC Ch. 13.3 - Prob. 13MC Ch. 13.3 - Prob. 14MC Ch. 13.3 - Prob. 15MC Ch. 13.3 - Prob. 16MC Ch. 13.3 - Prob. 17MC Ch. 13.3A - In the following figures, describe a sequence of...Ch. 13.3A - Prob. 2A Ch. 13.3A - In each of the following drawings, find...Ch. 13.3A - Prob. 4A Ch. 13.3A - AB is the image of a candle AB produced by a box...Ch. 13.3A - Prob. 6A Ch. 13.3A - Prob. 7A Ch. 13.3A - a. Explain why in a coordinate system a dilation...Ch. 13.3A - Prob. 9A Ch. 13.3A - Prob. 10A Ch. 13.3A - Prob. 11A Ch. 13.3A - Prob. 12A Ch. 13.3B - Prob. 1A Ch. 13.3B - Prob. 2A Ch. 13.3B - Prob. 4A Ch. 13.3B - Prob. 5A Ch. 13.3B - Prob. 6A Ch. 13.3B - Prob. 7A Ch. 13.3B - Prob. 8A Ch. 13.3B - Prob. 9A Ch. 13.3B - Prob. 11A Ch. 13.3B - Prob. 12A Ch. 13.4 - The following figure is a partial tessellation of...Ch. 13.4 - Prob. 2MC Ch. 13.4 - Prob. 3MC Ch. 13.4 - Prob. 4MC Ch. 13.4 - Prob. 5MC Ch. 13.4 - Prob. 6MC Ch. 13.4 - Prob. 7MC Ch. 13.4 - Prob. 10MC Ch. 13.4 - Prob. 11MC Ch. 13.4 - Prob. 12MC Ch. 13.4 - Prob. 13MC Ch. 13.4 - Prob. 14MC Ch. 13.4 - A student asks if the image seen through a...Ch. 13.4 - Jillian wants to know why a regular pentagon will...Ch. 13.4 - Prob. 18MC Ch. 13.4 - Prob. 19MC Ch. 13.4 - Prob. 20MC Ch. 13.4 - Prob. 21MC Ch. 13.4 - Prob. 22MC Ch. 13.4 - What dilation, if any, allows a line with equation...Ch. 13.4 - Prob. 1NAEP Ch. 13.4A - Prob. 1A Ch. 13.4A - Prob. 2A Ch. 13.4A - Prob. 3A Ch. 13.4A - Prob. 4A Ch. 13.4A - Prob. 5A Ch. 13.4A - Prob. 6A Ch. 13.4A - The dual of a regular tessellation is the...Ch. 13.4A - Prob. 8A Ch. 13.4A - Prob. 9A Ch. 13.4B - Prob. 6A Ch. 13.4B - Prob. 7A Ch. 13.CR - Complete each of the following motions. a. A...Ch. 13.CR - Prob. 2CR Ch. 13.CR - Prob. 3CR Ch. 13.CR - Prob. 4CR Ch. 13.CR - Given that STAR in the figure shown is a...Ch. 13.CR - Prob. 6CR Ch. 13.CR - Given that SNOSWO in the following figure,...Ch. 13.CR - Prob. 8CR Ch. 13.CR - Prob. 9CR Ch. 13.CR - Prob. 10CR Ch. 13.CR - If a translation determined by (x,y)(x+3,y2) is...Ch. 13.CR - Prob. 12CR Ch. 13.CR - Prob. 13CR Ch. 13.CR - Prob. 14CR Ch. 13.CR - Prob. 15CR Ch. 13.CR - Prob. 16CR Ch. 13.CR - Prob. 17CR Ch. 13.CR - For each of the following cases, find the image of...Ch. 13.CR - Prob. 19CR Ch. 13.CR - Prob. 21CR Ch. 13.CR - On a 1-m equilateral triangle pool table, a ball...Ch. 13 - NOW TRY THIS In Figure 3 use a compass and...Ch. 13 - Prob. 2NT Ch. 13 - Prob. 3NT Ch. 13 - Prob. 5NT Ch. 13 - Prob. 8NT

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To prove: The inequality A M + M B < A P + P B and show that M B = M B ′ and B P = B ′ P , and then use the Triangle Inequality applied to Δ A P B ′ , and that A, M , and B′ are collinear.

Solution Summary: The author illustrates how the Triangle Inequality is applied to Delta APBprime and that A, M, and B′ are collinear.

Concept explainers

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To prove:

The inequality AM+MB<AP+PB and show that MB=MB′ and BP=B′P, and then use the Triangle Inequality applied to ΔAPB′, and that A, M, and B′ are collinear.

Want to see the full answer?

Chapter 13 Solutions

To prove: The inequality A M + M B &lt; A P + P B and show that M B = M B ′ and B P = B ′ P , and then use the Triangle Inequality applied to Δ A P B ′ , and that A, M , and B′ are collinear.

Solution Summary: The author illustrates how the Triangle Inequality is applied to Delta APBprime and that A, M, and B′ are collinear.

Concept explainers

Videos

To prove: The inequality AM+MB<AP+PB and show that MB=MB′ and BP=B′P, and then use the Triangle Inequality applied to ΔAPB′, and that A, M, and B′ are collinear.

Want to see the full answer?

Chapter 13 Solutions

To prove: The inequality A M + M B < A P + P B and show that M B = M B ′ and B P = B ′ P , and then use the Triangle Inequality applied to Δ A P B ′ , and that A, M , and B′ are collinear.

To prove:

The inequality AM+MB<AP+PB and show that MB=MB′ and BP=B′P, and then use the Triangle Inequality applied to ΔAPB′, and that A, M, and B′ are collinear.