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!
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
angle (they are along the line l).
3. Calculate the angle marked with the question mark. Do not measure.
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.
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 _________________________
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.
A self-teaching worktext for 4th-5th grade that covers angles, triangles, quadrilaterals, cirlce, symmetry, perimeter, area, and volume. Lots of drawing exercises!
Download ($6.90). Also available as a printed copy.