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.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter6: Circles
Section6.4: Some Constructions And Inequalities For The Circle
Problem 12E
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Question
Draw a rhombus that is naturally associated with the straightedge and compass construc-tion of a ray dividing an
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.
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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