Download Angles-of-a-Triangle..

Investigating
Angles
in Triangles
Free Geometry lesson from
Bethany @
MathGeekMama.com
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Teaching Tips for Exploring the Angles in Triangles:
Materials Needed:
• Student handouts
• Construction paper
• Scissors
Interior angles:
The goal of this investigation is to discover that the sum of the angles inside a triangle is 180
degrees. This requires that students know that a straight line is equal to 180 degrees. If you ask before
starting and there is some debate or uncertainty, allow students to draw a line and measure with a
protractor. Or simply look at the protractor more closely.
After cutting out triangles for their investigation, be sure students mark the angles. This will be very
important because once they cut off the angles to measure them, 3 new triangles will be formed and
you don’t want them to have to guess which angle was actually a part of their original triangle.
Exterior angles:
The second investigation looks at adjacent exterior angles. You may point out (or students may
observe) that by extending one of the sides, a straight line is formed, and therefore the sum of the
adjacent interior angle and the new exterior angle will equal 180 degrees. This is important to remember,
and may help students with the investigation.
The goal of this is to see that the exterior angle is equal to the sum of the two interior angles
opposite (not touching) the exterior angle formed. I tried to draw a diagram to make it clear which
angles are to be compared (and which angles need to be cut off), but students may need clarification
on this. You may want to cut apart a triangle together as a class before letting students try with their
own triangles.
In addition, answers to the discussion questions are included at the end of this lesson.
Have Fun Exploring Triangles!
© 2016 MathGeekMama.com
Interior Angles of Triangles
Directions: Use a piece of construction paper to cut out 4 different triangles. They can be any size.
Then use your triangles to complete the investigation below.
Step 1:
Draw an gle markin gs in each corner of each triangle so that you know where the interior angles are. Then
cut the corners (angles) off of triangle 1. Lay the angles side by side along the line below and measure the
total (in degrees) using your protractor. Record the answer below. Then repeat the process for your other 3
triangles.
Triangle 1 interior angles are
equal to:
Triangle 2 interior angles are
equal to:
_____________ degrees
_____________ degrees
Triangle 3 interior angles are
equal to:
Triangle 4 interior angles are
equal to:
_____________ degrees
_____________ degrees
Step 2:
For any triangle, the sum of the interior angles is equal to: ________________________
© 2016 MathGeekMama.com
Exterior Angles of Triangles
Directions: Use a piece of construction paper to cut out 2 different triangles. They can be any size.
Then use your triangles to complete the investigation below.
Step 1:
The purpose of this investigation is to determine the angle outside of your t rian gle (either side will work).
For example, in the diagram below, we are trying to determine the measure of angle d. Place your first triangle
on the line below, similar to the diagram. Label your angles and then cut off the interior angles opposite
the e xterior an gle you are trying to measure. (For example, in the diagram below, we would cut off angles
a and b). Line up the 2 angles you cut off with the third interior angle to try and determine the measure of the
exterior angle. Do the same with your second triangle.
a
b
c
d
© 2016 MathGeekMama.com
Exterior Angles of Triangles
Step 2: Think About It…
1. How do the two interior angles compare to the exterior angle?
_______________________________________________________________________________________________________________________________________
2. Do you think this is true for any triangle? Why?
_______________________________________________________________________________________________________________________________________
3. Can you write a mathematical formula for the measure of the exterior angle?
_______________________________________________________________________________________________________________________________________
Step 3: Solve it. Find the measure of the angles indicated below.
b
60o
c
15o
a
90o
a = ______________
135o
115o
b = ______________
© 2016 MathGeekMama.com
80o
c = ______________
Interior Angles of Triangles
Directions: Use a piece of construction paper to cut out 4 different triangles. They can be any size.
Then use your triangles to complete the investigation below.
Step 1:
Answer Key
Draw an gle markin gs in each corner of each triangle so that you know where the interior angles are. Then
cut the corners (angles) off of triangle 1. Lay the angles side by side along the line below and measure the
total (in degrees) using your protractor. Record the answer below. Then repeat the process for your other 3
triangles.
Triangle 1 interior angles are
equal to:
Triangle 2 interior angles are
equal to:
___180_____ degrees
____180____ degrees
Triangle 3 interior angles are
equal to:
Triangle 4 interior angles are
equal to:
_____180____ degrees
_____180____ degrees
Step 2:
For any triangle, the sum of the interior angles is equal to: ___180 degrees______
© 2016 MathGeekMama.com
Exterior Angles of Triangles
Step 2: Think About It…
Answer Key
1. How do the two interior angles compare to the exterior angle?
______The two interior angles are equal to the exterior angle.__________________________________________________________
2. Do you think this is true for any triangle? Why?
________Yes, because the 3 interior angles equal 180o and the adjacent interior and exterior equal 180o. Therefore,
the two interior angles and the exterior angle are equal to 180o – the those angles._________
3. Can you write a mathematical formula for the measure of the exterior angle?
_Variables used here may vary, but it should be something like d = a + b, where d is the exterior angle and a and b
are the opposite interior angles. ._
Step 3: Solve it. Find the measure of the angles indicated below.
b
60o
c
15o
a
90o
a = ____150o____
135o
115o
b = ______20o_____
© 2016 MathGeekMama.com
80o
c = ____95o____
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