warm-up exercises bell work use the symmetric and ... notes to post.pdf · use the symmetric and...

Warm-Up Exercises

Use the symmetric and transitive properties of equality

respectively to complete the statements.

2. If AB = CD and CD = TU, then ? .

1. If m 1 = m 3, then m 3 = ? .

Bell Work

Warm-Up Exercises

Use a property of equality to complete the statement.

4. If m EFG = 28º and m GFH = 62º,

then ? + 62º = m EFG + m GFH.

3. If RS = WX, then ? + AB = ? + AB.

Bell Work

Warm-Up ExercisesNotes

Theorem: A statement that can be proven. Once it is proven, it can be used

as a reason in other proofs.

Proof: A logical argument that shows a statement is true.

Two-column proof: one type of proof that has numbered statements and

corresponding reasons that show an argument in logical order.

Warm-Up ExercisesEXAMPLE 1 Write a two-column proof

Write a two-column proof for

the situation in Example 4

from Lesson 2.5.

GIVEN: m 1 = m 3

PROVE: m EBA = m DBC

1. m 1 = m 32. m EBA = m 3 + m

3. m EBA = m 1 + m

1. Given

2. Angle Addition Postulate

3. Substitution Property of Equality

STATEMENT REASONS

4. m 1 + m 2 = m DBC 4. Angle Addition Postulate

5. m EBA = m DBC 5. Transitive Property of Equality

Warm-Up ExercisesGUIDED PRACTICE for Example 1

GIVEN : AC = AB + AB

PROVE : AB = BC

1. AC = AB + AB

2. AB + BC = AC

3. AB + AB = AB + BC

4. AB = BC

1. Given

2. Segment Addition Postulate

3.

4.

STATEMENT REASONS

1. Four steps of a proof are shown. Give the reasons

for the last two steps.

Warm-Up ExercisesNotes

Theorem 2.1 Congruence of Segments

Segment congruence is reflexive, symmetric, and transitive.

Theorem 2.1 Congruence of Angles

Angle congruence is reflexive, symmetric, and transitive.

If A B and B C, then A C.

If A B then B A.

For any angle A, B A C, A

If AB CD , then CD AB .

If AB CD and CD EF then AB EF .

For any segment AB, AB AB .

Warm-Up ExercisesEXAMPLE 2 Name the property shown

Name the property illustrated by the statement.

a. If R T and T P, then R P.

b. If NK BD , then BD NK .

Warm-Up ExercisesGUIDED PRACTICE for Example 2

2. CD CD

3. If Q V, then V Q.

Name the property illustrated by the statement.

Warm-Up ExercisesEXAMPLE 3 Use properties of equality

Prove this property of midpoints: If you know that M is

the midpoint of AB ,prove that AB is two times AM and

AM is one half of AB.

GIVEN: M is the midpoint of AB .

PROVE: a. AB = 2 AM

b.AM = AB21

Warm-Up Exercises

STATEMENT REASONS

EXAMPLE 3 Use properties of equality

1. M is the midpoint of AB.

2. AM MB

3. AM = MB

4. AM + MB = AB

1. Given

2. Definition of midpoint

3. Definition of congruent segments

4. Segment Addition Postulate

5. AM + AM = AB 5. Substitution Property of Equality

6. 2AM = ABa.

AM = AB217.b.

6. Distributive Property

7. Division Property of Equality

Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem

Walking down a hallway at the mall, you notice the

music store is halfway between the food court and

the shoe store. The shoe store is halfway between the

music store and the bookstore. Prove that the

distance between the entrances of the food court and

music store is the same as the distance between the

entrances of the shoe store and bookstore.

Shopping Mall


SOLUTION

STEP 1 Draw and label a diagram.

STEP 2 Draw separate diagrams to show mathematical

relationships.

STEP 3 State what is given and what is to be proved

for the situation.

Then write a proof.


GIVEN: B is the midpoint of AC .

C is the midpoint of BD .

PROVE: AB = CD

STATEMENT REASONS

1. B is the midpoint of AC .

C is the midpoint of BD .

1. Given

2. Definition of midpoint2. AB BC

3. BC CD 3. Definition of midpoint

5. AB = CD

4. AB CD 4. Transitive Property of Congruence

5. Definition of congruent segments

Warm-Up ExercisesDaily Homework Quiz

(Reflexive Prop. Of Eq.)2. ?

1. MA = TH ( ? )

Statements (Reasons)

1. Copy and complete the proof.

GIVEN: MA = TH

PROVE: MT = AH

Quick Check



1. Copy and complete the proof.

GIVEN: MA = TH

PROVE: MT = AH

3. MA + AT = AT + TH ( ? )

MA + AT = MT; AT + TH =AH4. ( ? )

Quick Check

5. (Substitution Prop. Of Eq.)?


2. Use the given information to

prove the statement.

PROVE: m 2 = 31o

GIVEN: m 1 + m 2 = 90 ;

m 1 = 59

o

o


ANSWER

(Subtraction Prop. Of Eq.)2. m 2 = 90 – m 1o

(Substitution Prop. Of Eq.)3. m 2 = 90 – 59o o

(Simplify)4. m 2 = 31o

(Given)1. m 1 + m 2 = 90 ; m 1 = 59 oo

Quick Check

Warm-Up Exercises

HomeworkHW: 2.6 (pg. 108-110) #1-3,8,10,16,19,21-24

For Tomorrow

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