Triangle Inequality Theorem and Triangle Sum

Triangle Sum and Inequality Therom

Sum of Angles in a Triangle

• A triangle has 3 angles that ADD together to equal 180 degrees.

• If you are given angles and they DO NOT ADD UP TO 180 degrees, then you CAN NOT make a Triangle.

Multiple Choice

The Sum of Angles in a Triangle Theorem states that the angles in a triangle ADD up to what degree?

• 90 Degrees

• 180 Degrees

• 270 Degrees

• 360 Degrees

Multiple Choice

Which Angle measurements create a Triangle?

• 60

  60

  61

• 90

  45

  45

• 100

  50

  50

• 90

  90

  80

Multiple Choice

Which Angle measurements does NOT create a Triangle?

• 60

  60

  60

• 90

  45

  45

• 50

  60

  40

• 50

  100

  30

Find Missing Angle

Step 1: Write as a SUM of 180

Step 2: Plug In and SOLVE

Ex: a + b + c = 180

a = 120

b = 34

120 + 34 + c = 180

154 + c = 180

c = 26 Degrees

Multiple Choice

Find the missing angle measure of Angle T.

• 71 Degrees

• 105 Degrees

• 109 Degrees

• 82 Degrees

Multiple Choice

Find the measure of the indicated angle.

• 95

• 85

• 35

• 45

Angles and Sides

• The smallest angle will be opposite the  shortest side

• While the largest angle will be opposite the longest side.

• A side is congruent to another side if it has an equal length.

Triangle Inequality

To form a triangle, the sum of any two side lengths MUST be GREATER THAN the last side length.

a + b > c

b + c > a

a + c > b

Multiple Choice

Can the following side measures form a triangle?
  4 cm, 7 cm, 10 cm 

• Yes
• No

Multiple Choice

Can the following side measures form a triangle?
  3 ft, 5 ft, 8 ft 

• Yes
• No