Year 2 Warm Up

For #1-2 find the rule, then find the next three terms in the sequence.

1. 2 ,-4,-10, -16, -22…

2. -8, -4, 0, 4, 8…

3. Find the slope of (-8, 7) and (-8, 6)

4. Find the slope of (-2, 7) and (-8, 7)

1. -6; -28,-34,-40

2. 4; 12,16,20

3. undefined

4. m=0

2.5 Angle Relationships Investigation 1 “The Linear Pair Conjecture” Step 1) Draw PQ with point R between points P

and Q. Step 2) Draw RS – Now you have a Linear Pair Step 3) Label the angles <1 and <2. Step 4) Use your protractor to measure <1 and

<2. Step 5) Compare your results for your two angles’

measures with your group or a classmate.

What do you notice about the two angles?

Linear Pair Conjecture

Angle Relationships

Linear Pair Conjecture – If two angles form a linear pair, then the measures of the angles add up to 180 degrees.

1 2

<1+<2=180 °

Angle Relationships

Investigation 2 “Vertical Angles Conjecture” Step 1) Draw two intersecting lines that are not

perpendicular onto patty paper. Label the angles as shown:

Which angles are vertical?

Step 2) Fold the patty paper so that one pair of vertical angles lie over each other.

Vertical Angles

Conjecture1

23

4

What do you notice about their measure?

Vertical Angles Conjecture: If two angles are vertical angles, then they are congruent.

12

34

<1=<3 <2=<4

Find the missing measures

Ex 1)

a bc

130°

a =

b =

c =

50°

130°

50°

Find the missing measures

Ex 2)

a

c65°

b

a =

b =

c =

90°

25°

90°

Find the missing measures

Ex 3)

b c

30°d50°

a

a =

b =

c =

d =

30°

100°

50°

100°

Algebra with Angles – Ex 1a) State the type of anglesb) State the relationshipc) Solve for x.d) Then find measure of each angle.

m<1 = 3x-40

2x-10 = m<2

Answer 1

The angles are vertical, therefore they are congruent. This means that the measures of each angle are equal.

m<1 = m<23x-40 = 2x – 10x – 40 = -10x = 30

Step 1: Set up the angle relationship.

Step 2: Substitute in values.

Step 3: Solve for x.

Step 4: Plug back in to find angle measures.

m<1 = 50° m<2 = 50°

m<1 = 3(30) - 40 m<2 = 2(30) - 10

Algebra with Angles – Ex 2

a) State the type of anglesb) State the relationshipc) Solve for x d) Find the measure of angle 1.

m<1 = 4x - 20

m<2 =x

Answer – Ex. 2

<1 and <2 form a line making them a linear pair which adds up to 180 degrees.

Therefore, m<1 +<2 = 180°(4x – 20) + (x) = 1805x – 20 = 1805x = 200x = 40°m<2 = 40°, m<1 = 140°

Step 1: Set up the angle relationship.

Step 2: Substitute in values.

Step 3: Solve for x.

Step 4: Plug back in to find angle measures.

Summary : Make a chart below showing the angle types(vertical, linear pair, and right angles), their relationships(congruent, supplementary, complementary), and a sketch for each.

Homework Homework 2.5 worksheet

Classwork 2.5 Worksheet and Bookwork p. 122 #1-6…you must

copy the pictures and show your work!!!

In Class Practice