Download Closed figure Consists of line segments

• Need Shape Sets
Launch: Connecting to Prior Knowledge: Finding an acceptable mathematical definition
for polygon turns out to be tricky. The basic idea is that a polygon is a closed figure
consisting of line segments connected at the endpoints, called vertices. Additionally,
starting at any vertex, the outline of a polygon can be traced completely without
visiting any vertex more than once and by returning to the starting point. Since
polygons consist of line segments, figures that are curved are not polygons. Figures
that have line segments that intersect at any point other than a vertex are not
polygons. Also, figures that are not closed cannot be polygons because they cannot be
traced by returning to the starting point.
Quick Start Expectations
1. Come in and sit quietly.
2. Fill in planner and HWRS:
Textbook: CMP3 Grade 7 Unit: Shapes and Designs
pp. 24-33: #2-4, 37-44, 46 (WS for #2)
3. Work on Warm-up :
1. Give two equivalent fractions for 8
12
2. Insert < , >, or = to write a true statement:
11
3
38
26
6
21
12
4
38
26
13
41
How would you describe the difference between the two groups?
Polygons are closed with straight sides;
non-polygons can be open with curved sides.
What test would you suggest for deciding if a figure is a polygon?
Tracing the edges to get back to the start without retracing or crossing a line segment.
What familiar objects have shapes like the polygon examples?
various road signs
What other shapes could be used as examples of
Quadrilaterals and octagons are polygons.
polygons and non-polygons?
Semicircles and squiggles are non-polygons.
Describe the key properties that define a polygon:
Closed figure
Connected by vertices (endpoints)
Consists of line segments (no curves)
Starting at any vertex, the outline of a polygon can be traced completely
without visiting any vertex more than one
and by returning to the starting point.
Group Activity:
Which polygon is it?
a. One team member picks a polygon from the shapes bag.
b. Think about its properties. Without naming it,
describe the shape including appropriate vocabulary:
vertex / vertices
angle
line segment
c. Other team members guess the correct polygon.
d. Take turns describing and guessing.
As a team use the Shapes Set (shown on pg. 9)
to answer the questions on page 10.
Record the answers in your journal.
ANSWERS:
Answers will vary.
Answers will vary.
A – all sides and angles are equal (equilateral triangle)
P – a pair of equal sides and equal angles (isosceles triangle)
I and T – no equal sides or angles.
Amount of groups will vary, including rectangles,
non-rectangle parallelograms, trapezoids, no parallel sides.
1. R, O, S have one pair of parallel sides (trapezoid)
2. Q doesn’t have any parallel sides,
but it is still a quadrilateral.
3. L has two sides of parallel sides – referred to as a parallelogram,
but can be a trapezoid.
Squares & Rectangles
• How are squares and rectangles the same?
They each have 4 sides and 4 angles.
• How are they different?
A square must have 4 equal sides and 4 equal angles.
Rectangles just need opposite sides equal and all angles equal.
• Is N a rectangle? Why or why not?
No, because it does not have 4 right angles.
• Is a rectangle a parallelogram? Why or why not?
Yes, it is a quadrilateral with opposite sides equal and opposite
angles of the same measure.
• Is a square a rectangle? Why or why not?
Yes, not only are opposite sides equal, but all sides are equal.
Homework:
Textbook: CMP3 Grade 7
Unit: Shapes and Designs
pp. 24-33 #2-4, 37-44, 46
Use WS for #2