how many triangles can i make? constructing triangles
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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
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