Upload
jesse-baldwin
View
218
Download
1
Tags:
Embed Size (px)
Citation preview
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
Classifying PolygonsClassifying PolygonsPRE-ALGEBRA LESSON 9-3PRE-ALGEBRA LESSON 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.
Classifying PolygonsClassifying PolygonsPRE-ALGEBRA LESSON 9-3PRE-ALGEBRA LESSON 9-3
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.
Classifying PolygonsClassifying PolygonsPRE-ALGEBRA LESSON 9-3PRE-ALGEBRA LESSON 9-3
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.
Classifying PolygonsClassifying PolygonsPRE-ALGEBRA LESSON 9-3PRE-ALGEBRA LESSON 9-3
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
Classifying PolygonsClassifying PolygonsPRE-ALGEBRA LESSON 9-3PRE-ALGEBRA LESSON 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
Problem Solving Strategy: Draw a DiagramProblem Solving Strategy: Draw a DiagramPRE-ALGEBRA LESSON 9-4PRE-ALGEBRA LESSON 9-4
(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
Problem Solving Strategy: Draw a DiagramProblem Solving Strategy: Draw a DiagramPRE-ALGEBRA LESSON 9-4PRE-ALGEBRA LESSON 9-4
Solutions
1. 2. 3.
4. 5.
9-4
Problem Solving Strategy: Draw a DiagramProblem Solving Strategy: Draw a DiagramPRE-ALGEBRA LESSON 9-4PRE-ALGEBRA LESSON 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
Problem Solving Strategy: Draw a DiagramProblem Solving Strategy: Draw a DiagramPRE-ALGEBRA LESSON 9-4PRE-ALGEBRA LESSON 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
Problem Solving Strategy: Draw a DiagramProblem Solving Strategy: Draw a DiagramPRE-ALGEBRA LESSON 9-4PRE-ALGEBRA LESSON 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