1. Constructing Triangles
How many Triangles Can I make?

2. Triangle Inequality Theorem
The third side of a triangle must be:
Less than the sum of the other two sides.
Greater than the difference of the other two sides.
4+6 = <10
6-4 = >2
9+6 = <15
9-6 = >3
9+4 = <13
9-4= >5 4 6 9

3. Example
Can we create a triangle using sides of length 3,4, and 5?
Can we construct a triangle using sides of length 4, 7, and 12?
Yes! Why?
No. Why?

4. 90 + 110 = 200 200>180 Angles in a Triangle
We learned that the angles in a triangle add to 180o.
Ex. If I have an angle that is 900 and another angle that is can I create a triangle? Why?
= 200
200>180
So these angle measures cannot create a triangle!

5. Exterior and Remote Interior Angles
An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side
Adjacent means next to or adjoining
For each exterior angle of a triangle, the two nonadjacent interior angles are called the remote interior angles

6. Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles
m∠1 = m∠2 + m∠3
Ex: If m∠2 = 45 and m∠3 = 55, what is m∠1?
m∠1 = = 100

7. Examples
Solve for x.
Solve for y.
50o
60o x 40 y
112o

8. Exterior Angles m∠1 + m∠2 + m∠3 = 360o
The exterior angles of a triangle add to 360o
∠ 2
∠ 1
∠ 3
m∠1 + m∠2 + m∠3 = 360o

9. Examples
Can I construct a triangle with an exterior angle of 850 and remote interior angles that are 35o and 60o ?
Can I construct a triangle with exterior angles 90o , 120o , and 80o ?
If two exterior angles of a triangle are 110o and 115o what is the measure of the third exterior angle?

10. Constructing triangles
Objective: To construct triangles using a protractor.
60º

11. Three ways to construct triangles.
When constructing triangles we need a combination of angles and lengths.
We can construct triangles with a compass if we have the lengths of the 3 sides (SSS). ( We won’t be looking at this one just yet)
We can construct triangles using a protractor if we have the length of 1 side and the measurement of 2 angles (ASA ).
We can construct triangles using a protractor if we have the length of 2 sides and the measurement of 1 angles ( SAS ).
Note: To construct triangles, we need to know the length of at least 1 side plus 2 other pieces of information.

12. Given one side and two angles (ASA):
Draw a triangle with one side 6cm and angles at each end of 30º and 70º.
Mark 70º
Mark 30º
6 cm

13. Given two sides and one angle ( SAS):
Draw a triangle with a side 12 cm and side 9 cm
with an angle of 75º between them.
Mark 75º
12 cm

14. Practice Problems
Construct the following triangles:
A S A Triangles
40º 7cm 50º
45º 6 cm 45º
20º 8cm 100º
60º 8cm 60º
110º 7 cm º
S A S Triangles
7cm 50º 4 cm
6 cm 45º 6 cm
8cm 100º 6 cm
8cm 60º 8 cm
7 cm º 6 cm