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Draw a rhombus that is naturally associated with the straightedge and compass construc-tion of a ray dividing an angle in half shown in Figure 14.27. b. Explain why the quadrilateral that you identify as a rhombus in part (a) really must be a rhombus, according to the definition of rhombus and according to the way it was constructed. c. Why does the construction in Figure 14.27 work? Use a special property of rhombuses to explain why the construction produces a ray that divides the given angle at P in half.

Draw a rhombus that is naturally associated with the straightedge and compass construc-tion of a ray dividing an angle in half shown in Figure 14.27. b. Explain why the quadrilateral that you identify as a rhombus in part (a) really must be a rhombus, according to the definition of rhombus and according to the way it was constructed. c. Why does the construction in Figure 14.27 work? Use a special property of rhombuses to explain why the construction produces a ray that divides the given angle at P in half.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 7AEXP
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Draw a rhombus that is naturally associated with the straightedge and compass construc-tion of a ray dividing an angle in half shown in Figure 14.27.

b. Explain why the quadrilateral that you identify as a rhombus in part (a) really must be a rhombus, according to the definition of rhombus and according to the way it was constructed.

c. Why does the construction in Figure 14.27 work? Use a special property of rhombuses to explain why the construction produces a ray that divides the given angle at P in half. 

ZXXXX Step 1: Starting with two rays that meet at a point P draw part of a circle centered at P. Let Q and R be the points where the circle meets the rays R Step 2: Keep the compass opened to the same radius Draw a circle centered at Q and another circle centered at R. Step 3: Draw a line through point P and the other point where the last two circles drawn meet. This line cuts the angle RPQ in half. Figure 14.27 Constructing an angle bisector.
Transcribed Image Text:ZXXXX Step 1: Starting with two rays that meet at a point P draw part of a circle centered at P. Let Q and R be the points where the circle meets the rays R Step 2: Keep the compass opened to the same radius Draw a circle centered at Q and another circle centered at R. Step 3: Draw a line through point P and the other point where the last two circles drawn meet. This line cuts the angle RPQ in half. Figure 14.27 Constructing an angle bisector.
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