EXTERIOR ANGLES

When the sides of a polygon are extended, other angles are formed.

The original angles are the interior angles.

The angles that form linear pairs with the interior angles are the exterior angles.

Angles

EXTERIOR ANGLE THEOREMAn exterior angle of a triangle…… is equal in measure to the sum of the measures of its two remote interior angles.

remote interior angles Exterior

angle

EXTERIOR ANGLE THEOREM(YOUR NEW BEST FRIEND)

The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles

3

2

1 4

exterior angle

remote interioranglesm<1 + m<2 = m<4

m 1 = m A + ∠ ∠m B ∠

EXTERIOR ANGLE THEOREM

EXAMPLES

m<G = 60 + 69m<FHG = 180 – 111 = 69 linear pair

EXAMPLES

x

82°

30° y

Find x & y

x = 68°y = 112°

y = 30 + 82y = 112˚

180 = 30 + 82 + x180 = 112 + x68˚ = x

EXAMPLESFind m JKM

2x – 5 = x + 70 x – 5 = 70 x = 75

m< JKM = 2(75) - 5m< JKM = 150 - 5m< JKM = 145˚

EXAMPLESSolve for y in the diagram.

Solve on your own before viewing the

Solution

4y + 35 = 56 + y3y + 35 = 563y = 21

y= 27

SOLUTION

EXAMPLESFind the measure of in the diagram shown.1

Solve on your own before viewing the

Solution

40 + 3x = 5x - 1040 = 2x - 1050 = 2x 25 = x

m < 1= 5x - 10m < 1= 5(25) - 10m < 1= 125 - 10m < 1= 115

SOLUTION

CHECKPOINT: COMPLETE THE EXERCISES.

SOLUTION

Right Scalene triangle

x + 70 = 3x + 10

70 = 2x + 1060 = 2x30 = x

3 (30) + 10 = 100˚

TRIANGLE INEQUALITIES

Make A Triangle

Construct triangle DEF.

D FF E

D E

D FF E

D E

Make A Triangle

Construct triangle DEF.

D E

Make A Triangle

Construct triangle DEF.

D E

Make A Triangle

Construct triangle DEF.

D E

Make A Triangle

Construct triangle DEF.

D E5 3

13

Q:What’s the problem with this?

A: The shorter segments can’t reach each other to complete the triangle. They don’t add up.

Make A Triangle

Construct triangle DEF.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Triangle Inequality Conjecture

Add the two smallest sides; they MUST be larger than the third side

for the triangle to be formed.

Make A TriangleCan the following lengths form a triangle?1.4 mm

5 mm10 mm

2.2 ft9 ft13 ft

5.10 mm3 mm6 mm

8. 8 m7 m1 m

9.9 mm2 mm1 mm

12.1 mm5 mm3 mm

3.5 cm cm4 cm

√𝟐4. 7 ft

15 ft ft

√𝟏𝟑6. 7 ft

7 ft ft

√𝟕

7.10 mm13 mm mm

√𝟓10.

12 mm22 mm mm

√𝟏𝟑

11.7 mm8 mm mm

√𝟏𝟐

In a triangle, if one side is longer than another side, then angle opposite the longer side is larger than the other.

Side-Angle Conjecture

Side-Angle

What’s the biggest side?What’s the biggest angle?What’s the smallest side?What’s the smallest angle?

C

B A

ba

c

bBaA

Side-Angle

92° 42°

46°

ab

c

Rank the sides from greatest to least.bca

Rank the angles from greatest to least.CAB

A

CB

7

5

4