4.1 & 4.2 A Notes

Type of ∆ Definition Picture

Equilateral Triangle

CL

AS

SIF

ICA

TIO

N B

Y S

IDE

S

All sides are

Type of ∆ Definition Picture

Isosceles Triangle

CL

AS

SIF

ICA

TIO

N B

Y S

IDE

S

At least 2 sides

base

leg leg

Type of ∆ Definition Picture

Scalene Triangle

CL

AS

SIF

ICA

TIO

N B

Y S

IDE

S

No sides are

Type of ∆ Definition Picture

EquiangularTriangle

CL

AS

SIF

ICA

TIO

N B

Y A

NG

LE

S

All angles are

Type of ∆ Definition Picture

Acute Triangle

CL

AS

SIF

ICA

TIO

N B

Y A

NG

LE

S

All angles are acute

Type of ∆ Definition Picture

Right Triangle

CL

AS

SIF

ICA

TIO

N B

Y A

NG

LE

S

One right angle leg

leghyp

oten

use

Type of ∆ Definition Picture

Obtuse Triangle

CL

AS

SIF

ICA

TIO

N B

Y A

NG

LE

S

One obtuse angle and 2 acute angles

Interior Angles – Angles inside a shape

Exterior Angles – Angles outside a shape

Corollary – Statement easily proved from another statement

a c

b

ac b

The sum of the measures of a triangle = _______180°

If two triangles have two angles that are _______,

then the third angle is also ___________.

A

B

C D

E

F

40° 40°60° 60°

80° 80°

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

a + b = 180°

b + c + d = 180°

b + c + d = a + b

c + d = a

The acute angles of a right triangle are

______________.complementary

a

c

a + c + 90 = 180°a + c = 90°

Classify the triangle by its sides and angles.

scalene right

Classify the triangle by its sides and angles.

equilateral

equiangular

Classify the triangle by its sides and angles.

isosceles

obtuse

4. Find the value of x. Then classify the triangle by its angles.

2x + 3x + 55 = 180

5x + 55 = 180 -55 -55

5x = 125

x = 25°5 5

50°

75°

acute

4. Find the value of x. Then classify the triangle by its angles.

4x – 5 + 3x + 5 + 40 = 180

7x + 40 = 180 -40 -40

7x = 140

x = 20°7 7

75°

65°

acute

4. Find the value of x. Then classify the triangle by its angles.

2x + 2 + 2x + 2 + 3x + 1 = 180

7x + 5 = 180 -5 -5

7x = 175

x = 25°7 7

52°52°

76°

acute

5. Find the measure of each exterior angle shown.

x + 80 = 3x – 22 -x -x .

102 = 2x

51° = x

2 2

80 = 2x – 22 +22 +22

3(51) – 22 = 131°

5. Find the measure of each exterior angle shown.

2x + 103 – x = 6x – 7

-x -x .

110 = 5x

22° = x5 5

103 = 5x – 7 +7 +7

x + 103 = 6x – 7

6(22) – 7 = 125°

5. Find the measure of each exterior angle shown.

2x + 3 + 51 = 4x + 8

-2x -2x .

46 = 2x23° = x

54 = 2x + 8

2x + 54 = 4x + 8

4(23) + 8 = 100°

6. Solve for the variables.

65°

y + 90 + 65 = 180

y = 25°

25°

y + 155 = 180

6. Solve for the variables.

55°

5y + 55 + 70 = 180

5y + 125 = 180 -125 -125

5y = 55

y = 11°5 5

7. Find the measure of each missing angle.

120°

120°60°30°

60°

30°

Ans: 30

**Project due Tomorrow! Bring your compass and ruler tomorrow!

HW ProblemSectio

nPage # Assignment Spiral ?

s

4.14.2a

221229

1-6, 14-18, 21-26, 32, 33, 3515, 16

1-4

4.1 # 26