HOW MANY TRIANGLES CAN I

MAKE?

Constructing Triangles

Triangle Inequality Theorem

The third side of a triangle must be:1.Less than the sum of the other two sides. 2.Greater than the difference of the other two

sides.

4 6

9

4+6 = 10 9<106-4 = 2 9>29+6 = 15 4<159-6 = 3 4>39+4 = 13 6<139-4= 5 6>5

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?

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 1100 can I create a triangle? Why?

90 + 110 = 200200>180

So these angle measures cannot create a triangle!

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

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 = 45 + 55 = 100

Examples

Solve for x.

Solve for y.

50o

60o x

40

y 112o

Exterior Angles

The exterior angles of a triangle add to 360o

∠ 1

∠ 2

∠ 3

m∠1 + m∠2 + m∠3 = 360o

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?

Constructing triangles

Objective: To construct triangles using a protractor.

60º

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.

Draw a triangle with one side 6cm and angles at each end of 30º and 70º.

6 cm

Mark 30º

Mark 70º

Given one side and two angles (ASA):

Draw a triangle with a side 12 cm and side 9 cm

with an angle of 75º between them.

Mark 75º

12 cm

Given two sides and one angle ( SAS):

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 45º

S A S Triangles

7cm 50º 4 cm

6 cm 45º 6 cm

8cm 100º 6 cm

8cm 60º 8 cm

7 cm 45º 6 cm