TODAY IN GEOMETRY…

Warm Up Learning Goal 1: 2.6 You will

write proofs using geometric theorems

Independent Practice – 10 minutes! Learning Goal 2: 2.7 Use

properties of special pairs of angles

Ch. 2 Review

Ch.2 Test Wednesday/Thursday! Ch. 1 Retakes before

Wednesday/Thurs.!

PROPERTIESREAL

NUMBERS SEGMENTS ANGLESREFLEXIVE

SYMMETRIC

TRANSITIVE

“equals itself”

“same in reverse”

“there’s a middle man”

WARM UP: Use the property to copy and complete the statement.1. Substitute Property of Equality:

If , then .

2. Symmetric Property of Equality:If , then .

3. Addition Property of Equality:If , then

4. Transitive Property of Equality:If and , then

20𝐶𝐷

𝑚∠2𝑚∠1

𝐴𝐵 𝐶𝐷

𝑚∠1𝑚∠3

TWO COLUMN PROOFS

using properties

EXAMPLE: Four steps of a proof are shown. Give the reasons for the last two steps.

Statement

Reason

Given: Prove:

1. 1. Given.

2. 2. Segment Add’n Postulate

3. 3. ____________________

𝐴 𝐶𝐵

4. 4. ____________________

Transitive Property

Subtraction Property

EXAMPLE: Four steps of a proof are shown. Give the reasons for the last two steps.

Statement

Reason

Given: , Prove:

1. , 1. Given.

2. 2. Segment Add’n Postulate

3. 3. ____________________

𝐴 𝐶𝐵

4. ___________________ 4. Simplify

Substitution Property

𝐴𝐶=11

5 6

PRACTICE: Which property listed is the reason for the last step in the proof?

10 minutesHOMEWORK #4:

Pg. 116: 5-11, 21 (Half sheet)

If finished, work on other assignments:

HW #1: Pg. 82: 3-18, 26-28, 47-54HW #2: Pg. 99: 3-8, 11-23HW #3: Pg. 109: 9-14

MORE PRACTICEAngle Pair

Relationships

PRACTICE:1. If

2. If

3. If

𝟏𝟏𝟐°𝟔𝟖°

𝟔𝟖°

𝟔𝟕°

𝟏𝟏𝟑°𝟏𝟏𝟑°

𝟕𝟏°𝟏𝟎𝟗°

𝟏𝟎𝟗°

PRACTICE: Complete the statement with

a.

b.

c.

d. If , then

¿¿¿

¿

Both are right angles.

Vertical angles are congruent.

Angles 8 and 6 are complementary.

Angles 5 and 4 are a linear pair.

PRACTICE: Find the values of x and y.

Vertical Angles are congruent!

Solve for x:

Solve for y:

PRACTICE: Find the values of x and y.

Adjacent angles are linear pairs!

Solve for x:

3 𝑥+504 𝑥+322 𝑦

3 𝑦+30

Solve for y:

HOMEWORK #5:

Pg. 127: 3-6, 8-11, 17-21, 28-29

If finished, work on other assignments:

HW #1: Pg. 82: 3-18, 26-28, 47-54HW #2: Pg. 99: 3-8, 11-23HW #3: Pg. 109: 9-14HW #4: Pg. 116: 5-11, 21 (in class work)