Download Additional Examples Lesson 3-5

Additional Examples
1
Lesson 3-5
EXAMPLE
Name the polygon. Then identify its vertices, sides,
and angles.
A
E
B
D
C
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The polygon can be named clockwise or counterclockwise, starting
at any vertex.
Possible names are ABCDE and EDCBA.
Its vertices are A, B, C, D, and E.
Its sides are AB or BA, BC or CB, CD or DC, DE or ED, and EA or AE.
Its angles are named by the vertices, lA (or lEAB or lBAE), lB (or
lABC or lCBA), lC (or lBCD or lDCB), lD (or lCDE or lEDC),
and lE (or lDEA or lAED).
Geometry, Chapter 3
43
Additional Examples
© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
2
Lesson 3-5
EXAMPLE
Classify the polygon below by its sides. Identify it
as convex or concave.
Starting with any side, count the number of sides clockwise around
the figure. Because the polygon has 12 sides, it is a dodecagon.
Think of the polygon as a star. If you draw a diagonal connecting two
points of the star that are next to each other, that diagonal lies
outside the polygon, so the dodecagon is concave.
The diagonal contains points
outside the polygon.
Geometry, Chapter 3
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Additional Examples
3
EXAMPLE
Lesson 3-5
Find the sum of the measures of the angles of a decagon.
A decagon has 10 sides, so n ≠ 10.
Sum ≠ (n – 2)(180)
Polygon Angle-Sum Theorem
≠ (10 – 2)(180) Substitute 10 for n.
≠ 8 • 180
Simplify.
≠ 1440
© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
4
EXAMPLE
Find mlX in quadrilateral XYZW.
Y
X
W
100
Z
The figure has 4 sides, so n ≠ 4.
mlX ± mlY ± mlZ ± mlW ≠ (4 – 2)(180) Polygon Angle-Sum
Theorem
mlX ± mlY ± 90 ± 100 ≠ 360
mlX ± mlY ± 190 ≠ 360
Simplify.
mlX ± mlY ≠ 170
Subtract 190 from each
side.
mlX ± mlX ≠ 170
Substitute mlX for
mlY.
2mlX ≠ 170
mlX ≠ 85
Geometry, Chapter 3
Substitute.
Simplify.
Divide each side by 2.
45
Additional Examples
5
EXAMPLE
A regular hexagon is inscribed in a rectangle.
Explain how you know that all the angles labeled l1 have
equal measures.
1
2
2
2
2
1
1
© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Lesson 3-5
1
Sample: The hexagon is regular, so all its angles are congruent. An
exterior angle is the supplement of a polygon’s angle because they
are adjacent angles that form a straight angle. Because supplements
of congruent angles are congruent, all the angles marked l1 have
equal measures.
Additional Examples
1
Lesson 3-6
EXAMPLE
Use the slope and y-intercept to graph the line
y ≠ –2x ± 9.
When an equation is written in the form y ≠ mx ± b, m is the slope
and b is the y-intercept. In the equation y ≠ –2x ± 9, the slope is –2
and the y-intercept is 9.
9
Move down 8
2 units.
7
6
5
4
3
2
1
5
y
Start at (0, 9).
Move right
1 unit.
x
3 1 0 1 2 3 4 5 6
1
Geometry, Chapter 3
46