This lesson lets students find (by measuring) that angle sum in a triangle is 180°. The lesson also contains a simple proof of this fact and varied exercises.
The angle sum of a Triangle is 180° - lesson with proof & varied exercises
1. Draw ANY triangle you like here.
(Use a ruler!) Measure all its
angles. Calculate the angle sum.
It is ______°.
2. Draw another triangle here.
Measure all its angles.
Calculate the angle sum.
It is ______°.
| Above, you probably made a guess that the sum of the
angles in a triangle is 180°. That is true. Here is a proof for it. Proof means that we use already established principles to prove that some new statement is always true. See if you can understand the reasoning in this proof! |
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Angles A and A' are corresponding angles, therefore ∠A = ∠A'. So, the angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'. The three angles A', B', and C' form together a
straight
angle (they are along the line l). |
3. Calculate the angle marked with the question mark. Do not measure.
a.
 |
b.
 |
c.
 |
4. A certain triangle has three equal angles.
What is the measure of each angle? _______°
Draw one using your protractor.
Make each of its sides 5 cm long.
This triangle has a special name.
What is it?
5. Can you draw a triangle that has
two obtuse angles?
Why or why not?
6. a. Draw a triangle
with 65° and 50° angles, with
a 7.5-cm side between those two
angles.
Start out by drawing the 7.5-cm
side.
b.
Calculate the third angle. It is _______°.
Then measure from your triangle to
check.
c. Classify your triangle according to its
sides and angles:
It is _________________________
and _________________________.
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This lesson is taken from Maria Miller's book Math Mammoth Geometry 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
