Classifying Polygons
PRE-ALGEBRA LESSON 9-3
(For help, go to Lesson 9-2.)
For the angle measures given, classify the angle as acute, right, or obtuse.
1. 85°
2. 95°
3. 160°
4. 90°
5. 36°
6. 127°
Check Skills You’ll Need
9-3
Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Solutions
1. acute
2. obtuse
3. obtuse
4. right
5. acute
6. obtuse
9-3
Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Classify the triangle by its sides and angles.
The triangle has no congruent sides and one obtuse angle.
The triangle is a scalene obtuse triangle.
Quick Check
9-3
Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Name the types of quadrilaterals that have at least
one pair of parallel sides.
All parallelograms and trapezoids have at least one pair of
parallel sides.
Parallelograms include rectangles, rhombuses, and squares.
Quick Check
9-3
Classifying Polygons
PRE-ALGEBRA LESSON 9-3
A contractor is framing the wooden deck shown below in the
shape of a regular dodecagon (12 sides). Write a formula to find the
perimeter of the deck. Evaluate the formula for a side length of 3 ft.
To write a formula, let x = the length of each side.
The perimeter of the regular dodecagon is
x + x + x + x + x + x + x + x + x + x + x + x.
Therefore a formula for the perimeter is P = 12x.
P = 12x
Write the formula.
= 12(3)
Substitute 3 for x.
= 36
Simplify.
For a side length of 3 ft, the perimeter is 36 ft.
9-3
Quick Check
Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Name the following.
1. a type of triangle that has at least two congruent sides and
one right angle
isosceles right triangle
2. a type of quadrilateral that can have opposite sides parallel
and no right angles
parallelogram, rhombus
3. Write a formula for the perimeter of a regular heptagon (7
sides). Evaluate for a side of 12 in.
P = 7x; 84 in.
9-3
Problem Solving Strategy: Draw a Diagram
PRE-ALGEBRA LESSON 9-4
Draw several different quadrilaterals. Connect the midpoints of the
sides of each figure. Write a sentence explaining in what way the
figures inside the quadrilaterals are alike.
Sample answer
They are all parallelograms.
9-4
Problem Solving Strategy: Draw a Diagram
PRE-ALGEBRA LESSON 9-4
(For help, go to Lesson 9-3.)
Sketch each figure.
1. equilateral triangle
2. rectangle
4. hexagon
5. octagon
3. pentagon
Check Skills You’ll Need
9-4
Problem Solving Strategy: Draw a Diagram
PRE-ALGEBRA LESSON 9-4
Solutions
1.
2.
4.
5.
3.
9-4
Problem Solving Strategy: Draw a Diagram
PRE-ALGEBRA LESSON 9-4
How many diagonals does a nonagon have?
One strategy for solving this problem is to draw a diagram and
count the diagonals. A nonagon has nine sides.
You can draw six diagonals from one vertex of a nonagon.
AH, AG, AF, AE, AD, and AC are
some of the diagonals.
9-4
Problem Solving Strategy: Draw a Diagram
PRE-ALGEBRA LESSON 9-4
(continued)
You can organize your results as you
count the diagonals. Do not count a
diagonal twice. (The diagonal from A to
C is the same as the one from C to A.)
Then find the sum of the numbers
of diagonals.
A nonagon has 27 diagonals.
Vertex Number of Diagonals
6
A
6
B
5
C
4
D
E
3
F
2
G
1
H
0
I
0
Total
27
Quick Check
9-4
Problem Solving Strategy: Draw a Diagram
PRE-ALGEBRA LESSON 9-4
Solve.
1. How many diagonals does a quadrilateral have?
2 diagonals
2. How many triangles can you form if you draw all the
diagonals from one vertex of a pentagon?
3 triangles
3. How many triangles can you form if you draw all the
diagonals of a rectangle?
8 triangles
9-4