TRIANGLE-SUM THEOREM

During this lesson, you will:Find the sum of the angles of a triangleUse exterior angles of triangles

EQUIANGULAROBTUSE

RIGHT ACUTE

Classify each triangle based upon its angle measures:

INVESTIGATION

3

THEOREM

The sum of the measures of the interior angles of any triangle is 180º ▲ Sum = 180.

A

B

C

mA + m B + m C = 180

INVESTIGATIVE RESULTS:

Triangle Sum Conjecture:

X Y

Z

48º 67º

Find m Z

48 + 67 + mZ = 180

115 + mZ = 180

mZ = 65

Ex. 1

mX + mY + mZ = 180

cº

aºbº

A

C

B

D

70ºFind the values of a, b and c.

Find cc + 70 = 90c = 20º

Find a. Use Triangle Sum a + mADC + c = 180a + 90 + 20 = 180a + 110 = 180

a = 70º

b = 20º

Find b. Use Triangle Sum

EX. 2Ex. 2

7

Use your triangle sum conjecture to calculate the measure of the third angle in each triangle below.

Third Angle Conjecture:If two angles of one triangle are equal in measure to two angles of another triangle, then the remaining angles _____________________.

A

B C

Exterior Angle Theorem

The measure of an exterior angle in any triangle equals the

sum of the two

remote interior angles.

x

m x = m 1 + m 2

1

2 3

Remote interior angles Exterior angle

Geometry Mrs. McConaughy 9

1. Measure the angles of your triangle that you traced.2. Extend one side of your triangle:

3. Measure that exterior angle

Examples: x

y 135

x + y = _____

x = ____

30

x

x 144

x

x

90 45

x = ____

x = ____

Justify your answer.