Home - HomeschoolMath.net

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!
  We draw a line parallel to AB that passes
through point C.

Angles C and C' are vertical angles,
therefore ∠C = ∠C'.

Angles B and B' are corresponding angles,
therefore ∠B = ∠B'.

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).
So, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.

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 _________________________.


Calculate the angle marked with “?”.

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.

Math Mammoth Geometry 1

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.

=> Learn more and see the free samples!

See more topical Math Mammoth books

Math Lessons menu