Monday, September 8Objective

SWBAT-

Find measures of adjacent angles as well as bisected angles.

DO NOW

Write two names for the angles, then name the vertex of the angle

1.4 Angle Addition PostulateAgenda:

• Do Now (12 min)

Work and SolveReview Grades

• Introduction to New Material (10 min)

Angles! Addition Postulate and Angle Bisectors

• Guided Practice (12 min)

Finding the measure of adjacent angles

• Independent Practice (12 min)

Finding measure of adjacent angles

• Exit Ticket (5 min)

Top Ten Results

1.4 Angle Addition PostulateWhat is one name for this angle?

A

G P

HWhat is the measure of this angle?

Name three different angles

75°

1.4 Angle Addition PostulateWhat would be the measure of ∠𝑃𝐺𝐴?

A

G P

HWhat would be the measure of ∠𝐴𝐺𝐻?

75°

130°

1.4 Angle Addition Postulate

1.4 Angle Addition Postulate

G

H J

K

Given: m∠GHK = 95

m∠GHJ = 114.

Find: m∠KHJ.

The Angle Addition Postulate tells us:

𝑚∠𝐺𝐻𝐾 + 𝑚∠𝐾𝐻𝐽 = 𝑚∠𝐺𝐻𝐽

95 + 𝑚𝐾𝐻𝐽 = 114

𝑚∠𝐾𝐻𝐽 = 19.

95°

114°

19°

Plug in what you know.

Solve.−95 −95

1.4 Angle Addition Postulate

This is a special example, because the two adjacent

angles together create a straight angle.

Predict what mABD + mDBC equals.

∠ABC is a straight angle, therefore m∠ABC = 180.

𝑚∠𝐴𝐵𝐷 + 𝑚∠𝐷𝐵𝐶 = 𝑚∠𝐴𝐵𝐶

134 + 𝑚∠𝐷𝐵𝐶 = 180

A B C

D

134°

−46

46°

Given ABC is a straight

angle, find mABC :

−46

𝑚∠𝐷𝐵𝐶 = 46

1.4 Angle Addition Postulate

R

S T

V

Given:

mRSV = x + 5

mVST = 3x - 9

mRST = 68

Find x.

mRSV + mVST = mRST

x + 5 + 3x – 9 = 68

4x- 4 = 68

4x = 72

x = 18

Set up an equation using the Angle Addition

Postulate.

Plug in

what you

know.Solve.

Now that you know x = 18, find mRSV and mVST.+4 +4

4 4 mRSV = x + 5

mRSV = 18 + 5 = 23

mVST = 3x - 9

mVST = 3(18) – 9 = 45

1.4 Angle Addition Postulate

1.4 Angle Addition Postulate

An angle bisector is a ray that divides an angle into 2 congruent adjacentangles.

𝐵𝐷 is an angle bisector of ∠𝐴𝐵𝐶.

B

A

C

D50°

50°

1.4 Angle Addition Postulate

* If they are congruent, set them equal to each other, then solve!

𝑥 + 40 = 3𝑥 − 20

40 = 2𝑥 − 20

60 = 2𝑥

30 = 𝑥

B

A

C

D

𝐵𝐷 bisects ABC. Find mABD and mABC

−𝑥 −𝑥

+20 +20

2 2

𝑚𝐴𝐵𝐷 = 𝑥 + 40

𝑚𝐴𝐵𝐶 = 140

= 30 + 40

= 70

1.4 Angle Addition Postulate

1.4 Angle Addition Postulate

𝑥 = 12𝑚∠𝐴𝐵𝐶 = 98° 𝑥 = 9

𝑚∠𝐴𝐵𝐶 = 112°

𝑚∠𝐶𝐸𝐷 = 15°

1.4 Angle Addition Postulate

Albert A. Michelson used the concept of angle bisectors and lasers to try to find the absolute speed of the Earth through space in what is now called the “most famous failed experiment”. It had the most precise instruments at the time. The speed of light was calculated and it helped pave the way for Einstein, planting the seed to the theory of relativity

1.4 Angle Addition Postulate

1.4 Angle Addition Postulate

1.4 Angle Addition Postulate