EXAMPLE 3 Find side lengths ALGEBRA A table is shaped like a regular hexagon. The expressions shown represent side lengths of the on: hexagonal table. Find the length of a side. (3x + 6) in. Solution (4x- 2) in. First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent. 3x + 6 = 4x – 2 Write equation. 6 = x- 2 Subtract 3x from each side. 8 - x Add 2 to each side. Then find a side length. Evaluate one of the expressions when x 8. 3.x + 6 = 3(8) + 6 = 30 • The length of a side of the table is 30 inches.
EXAMPLE 3 Find side lengths ALGEBRA A table is shaped like a regular hexagon. The expressions shown represent side lengths of the on: hexagonal table. Find the length of a side. (3x + 6) in. Solution (4x- 2) in. First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent. 3x + 6 = 4x – 2 Write equation. 6 = x- 2 Subtract 3x from each side. 8 - x Add 2 to each side. Then find a side length. Evaluate one of the expressions when x 8. 3.x + 6 = 3(8) + 6 = 30 • The length of a side of the table is 30 inches.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Can you help me with #1-14 please
Transcribed Image Text:EXAMPLE 3
Find side lengths
READ VOCABULARY
.............. ..
Hexagonal means
"shaped like a hexagon."
xy ALGEBRA A table is shaped like a regular hexagon.
The expressions shown represent side lengths of the
hexagonal table. Find the length of a side.
(3x + 6) in.
Solution
(4х — 2) in
First, write and solve an equation to find
the value of x. Use the fact that the sides
of a regular hexagon are congruent.
3x + 6 = 4x – 2
Write equation.
6 = x – 2
Subtract 3x from each side.
8 = x
Add 2 to each side.
Then find a side length. Evaluate one of the expressions when x = 8.
3x + 6 = 3(8) + 6 = 30
• The length of a side of the table is 30 inches.
GUIDED PRACTICE
for Example 3
3. The expressions 8y° and (9y – 15)° represent the measures of two of the
angles in the table in Example 3. Find the measure of an angle.
1.6 EXERCISES
HOMEWORK
KEY
= See WORKED-OUT SOLUTIONS
Exs. 13, 19, and 33
* = STANDARDIZED TEST PRACTICE
Exs. 2, 7, 37, 39, and 40
SKILL PRACTICE
1. VOCABULARY Explain what is meant by the term n-gon.
2. * WRITING Imagine that you can tie a string tightly around a polygon.
If the polygon is convex, will the length of the string be equal to the
distance around the polygon? What if the polygon is concave? Explain.
IDENTIFYING POLYGONS Tell whether the figure is a polygon. If it is not,
explain why. If it is a polygon, tell whether it is convex or concave.
EXAMPLE 1
**............
for Exs. 3-7
3.
4.
5.
6.
7. * MULTIPLE CHOICE Which of the figures is a concave polygon?
©
D
44
Chapter 1 Essentials of Geometry
Transcribed Image Text:EXAMPLE 2
CLASSIFYING Classify the polygon by the number of sides. Tell whether the
polygon is equilateral, equiangular, or regular. Explain your reasoning.
for Exs. 8-14
8.
9.
1 in.
1 in.
10.
1 in.
/1 in.
1 in.
11.
(13.
12.
5 m
4 ml
5 m
14. ERROR ANALYSIS Two students were asked to draw a regular hexagon, as
shown below. Describe the error made by each student.
Student A
Student B
15. O ALGEBRA The lengths (in inches) of two sides of a regular pentagon
are represented by the expressions 5x – 27 and 2x – 6. Find the length
of a side of the pentagon.
EXAMPLE 3
for Exs. 15-17
16. O ALGEBRA The expressions (9x + 5)° and (11x – 25)° represent the
measures of two angles of a regular nonagon. Find the measure of an
angle of the nonagon.
17. O ALGEBRA The expressions 3x - 9 and 23 – 5x represent the lengths
(in feet) of two sides of an equilateral triangle. Find the length of a side.
USING PROPERTIES Tell whether the statement is always, sometimes, or
never true.
18. A triangle is convex.
(19.) A decagon is regular.
20. A regular polygon is equiangular.
21. A circle is a polygon.
22. A polygon is a plane figure.
23. A concave polygon is regular.
DRAWING Draw a figure that fits the description.
24. A triangle that is not regular
25. A concave quadrilateral
26. A pentagon that is equilateral but not equiangular
27. An octagon that is equiangular but not equilateral
ALGEBRA Each figure is a regular polygon. Expressions are given for
two side lengths. Find the value of xr.
28.
29.
x? + 3x
30.
2+2x+ 40
x² + x + 2
-x+ 190
1.6 Classify Polygons
45
.......
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