page 248 #1-9 answers. pre-algebra 5-4 polygons pre-algebra homework page 248 #10-15
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Page 248 #1-9 ANSWERS
Pre-Algebra
5-4 Polygons
Pre-Algebra Homework
Page 248
#10-15
Pre-Algebra
5-4 Polygons
Student Learning Goal
ChartLesson Reflection for
Chapter 5 Sections 4 & 5
Pre-Algebra Learning GoalStudents will
understand plane geometry through plane figures and
patterns in geometry.
Pre-Algebra
5-4 PolygonsStudents will understand plane geometry
through plane figures and patterns in geometry by completing the following:
• Learn to classify and name figures (5-1)• Learn to identify parallel and perpendicular lines and the angles
formed by a transversal (5-2)• Learn to find unknown angles in triangles (5-3)• Learn to classify and find angles in polygons. (5-4)
• Learn to identify polygons in the coordinate plane. (5-5)
Pre-Algebra
5-4 Polygons
Learning Goal Assignment
Learn to classify and find angles in polygons.
Pre-Algebra
5-4 Polygons5-4 Polygons
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
5-4 Polygons
Vocabularypolygon
regular polygon
trapezoid
parallelogram
rectangle
rhombus
square
Pre-Algebra
5-4 Polygons
Pre-Algebra
5-4 Polygons
nn-gon
8Octagon
7Heptagon
6Hexagon
5Pentagon
4Quadrilateral
3Triangle
Number of SidesPolygon
Pre-Algebra
5-4 Polygons
Additional Example 1A: Finding Sums of the Angle Measures in Polygons
A. Find the sum of the angle measures in a hexagon.
4 • 180° = 720°
4 triangles
Divide the figure into triangles.
Pre-Algebra
5-4 Polygons
Try This: Example 1A
A. Find the sum of the angle measures in a hexagon.
4 • 180° = 720°
4 triangles
Divide the figure into triangles.
Pre-Algebra
5-4 Polygons
Additional Example 1B: Finding Sums of the Angle Measures in Polygons Continued
B. Find the sum of the angle measures in a octagon.
6 • 180° = 1080°
6 triangles
Divide the figure into triangles.
Pre-Algebra
5-4 Polygons
B. Find the sum of the angle measures in a heptagon.
5 • 180° = 900°
5 triangles
Try This: Example 1B
Divide the figure into triangles.
Pre-Algebra
5-4 Polygons
The pattern is that the number of triangles is always 2 less than the number of sides. So an n-gon can be divided into n – 2 triangles. The sum of the angle measures of any n-gon is 180°(n – 2).
All the sides and angles of a regular polygon have equal measures.
Pre-Algebra
5-4 PolygonsAdditional Example 2A: Finding the Measure of Each
Angle in a Regular Polygon
Find the angle measures in the regular polygon.
6 congruent angles
6x = 180°(6 – 2)
6x = 180°(4)
6x = 720°
6x 6
720°6
=
x = 120°
Pre-Algebra
5-4 Polygons
Try This: Example 2A
Find the angle measures in the regular polygon.
5 congruent angles
5a = 180°(5 – 2)
5a = 180°(3)
5a = 540°
5a5
540°5
=
a = 108°
a°
a°a°
a°
a°
Pre-Algebra
5-4 PolygonsAdditional Example 2B: Finding the Measure of Each
Angle in a Regular Polygon
Find the angle measures in the regular polygon.
4 congruent angles
4y = 180°(4 – 2)
4y = 180°(2)
4y = 360°
y = 90°
4y 4
360°4
=
Pre-Algebra
5-4 Polygons
Find the angle measures in the regular polygon.
8 congruent angles
8b = 180°(8 – 2)
8b = 180°(6)
8b = 1080°
8b 8
1080° 8
=
b = 135°
b°
b°
b° b°
b°
b°
b°b°
Try This: Example 2B
Pre-Algebra
5-4 Polygons
Additional Example 3A: Classifying Quadrilaterals
quadrilateral
parallelogram
rectangle
rhombus
square
Four-sided polygon
2 pairs of parallel sides
4 right angles
4 congruent sides
4 congruent sides and 4 right angles
Give all the names that apply to the figure.
Pre-Algebra
5-4 PolygonsAdditional Example 3B: Classifying Quadrilaterals
Continued
Give all the names that apply to the figure.
quadrilateral
parallelogram
rhombus
Four-sided polygon
2 pairs of parallel sides
4 congruent sides
Pre-Algebra
5-4 Polygons
Try This: Example 3A
Give all the names that apply to the figure.
quadrilateral
parallelogram
rectangle
Four-sided polygon
2 pairs of parallel sides
4 right angles
A.
Pre-Algebra
5-4 Polygons
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
B.
Try This: Example 3B
GRAPH PAPER RECOMMENDED!
Additional Example 3A: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)
parallelogram
CD || BA and BC || AD
Try This: Example 3A
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3)
parallelogram
A
CB
D
CD || BA and BC || AD
B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2)
parallelogram, rectangle, rhombus, square
Additional Example 3B: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
TU || SR and ST || RUTURU, RURS, RSST and STTU
B. E(1, 5), F(7, 5), G(6, 1), H(2, 1)
trapezoid
E F
H G
EF || HG
Try This: Example 3B
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
C. G(1, –1), H(1, –2), I(3, –3), J(3, 1)
trapezoid
Additional Example 3C: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
GH || JI
C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4)
parallelogram, rectangle, rhombus, square
X
W
Y
Z
ZW || YX and WX || ZYWXZW, XYWX, YZXY and ZWYZ
Try This: Example 3C
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0)
parallelogram, rectangle
Additional Example 3D: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
WZ || XY and WX || ZYWZZY, ZYXY, XYWX and WXWZ
D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1)
parallelogram, rectangle R
S
U
T
TU || SR and ST || RUTURU, RURS, RSST and STTU
Try This: Example 3D
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.