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Transcript
Geometry
Unit 5
How many different triangles, if any, can be
drawn with one 20° angle, one 40° angle, and
one 120° angle?
a. 0 triangles
b. Exactly 1 triangle
c. Exactly 2 triangles
d. Infinitely many triangles
Similar figures - side lengths are
proportional, but the angles
remain the same.
Similar Figures Review
18 ft
10 ft
Standard
CC.7.G.2. Draw geometric shapes with given conditions. Focus on
constructing triangles from three measures of angles or sides,
noticing when the conditions determine a unique triangle, more
than one triangle, or no triangle.
Essential Question
• How do I know when conditions will form one
triangle, no triangle, or more than one
triangle?
Discovery
Try to make triangles using the following colors.
Write down if you are able to make a triangle with the colors given.
5 cm, 7 cm, and 10 cm
2 cm, 2 cm, 15 cm
2 2 cm, 5 cm, 12cm
5 cm, 14 cm, and 15 cm
5 cm, 5 cm, and 10 cm
Pink, Green, Yellow
Dk green, Dk green, Blue
Dk green, Pink, Purple
Pink, Orange, Blue
Pink, Pink, Yellow
Yes
No
No
Yes
No
What can you conclude about the side lengths of triangles?
The two SHORTER SIDES must add up
to be LONGER than the longest side.
Try out your conclusion with other side lengths.
You
1)
3)
The two SHORTER SIDES must add up
Try…to be LONGER than the longest side.
2)
4)
Task
The two SHORTER SIDES must add up
to be LONGER than the longest side.
No
Yes
It must be longer than 2m,
but shorter than 18m
No
No
It must be longer than 6 in,
but shorter than 34 in
Find the range of the third
side of each triangle below.
Application of the Concept
Two miles long each because the two shorter sides must add up to be longer than the
longest side and all sides must add up to be 6 miles.
It must be longer than 7 feet, but shorter than 17 feet.
The two SHORTER SIDES must add up
to be LONGER than the longest side.
Closing
• How do you know when a triangle can be formed when given
various side lengths?
Any two sides of a triangle will add up to be longer
than the other side.
• How do you know when and how many triangles can be
formed when given three angle measurements?
All angles in a triangle must add up to 180°.
Triangles with the same angle measurements can
have varying side lengths (similar figures).
Exploragons
Contest
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