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

Classifying PolygonsClassifying PolygonsPRE-ALGEBRA LESSON 9-3PRE-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


Solutions

1. acute 2. obtuse 3. obtuse

4. right 5. acute 6. obtuse

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

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

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.Quick Check

9-3


Name the following.

1. a type of triangle that has at least two congruent sides and one right angle

2. a type of quadrilateral that can have opposite sides parallel and no right angles

3. Write a formula for the perimeter of a regular heptagon (7 sides). Evaluate for a side of 12 in. P = 7x; 84 in.

isosceles right triangle

parallelogram, rhombus

9-3

Problem Solving Strategy: Draw a DiagramProblem Solving Strategy: Draw a DiagramPRE-ALGEBRA LESSON 9-4PRE-ALGEBRA LESSON 9-4

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.

They are all parallelograms.

Sample answer


(For help, go to Lesson 9-3.)

Sketch each figure.

1. equilateral triangle 2. rectangle 3. pentagon

4. hexagon 5. octagon

Check Skills You’ll Need

9-4


Solutions

1. 2. 3.

4. 5.

9-4


How many diagonals does a nonagon have?

AH, AG, AF, AE, AD, and AC are some of the diagonals.

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.

9-4


(continued)

A nonagon has 27 diagonals.

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.

Vertex Number of DiagonalsABCDEFGHI

665432100

Total 27

Quick Check

9-4


Solve.

1. How many diagonals does a quadrilateral have?

2. How many triangles can you form if you draw all the diagonals from one vertex of a pentagon?

3. How many triangles can you form if you draw all the diagonals of a rectangle?

8 triangles

2 diagonals

3 triangles

9-4

Documents

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