Tuesday, September 17th

1. Fill in the Proofs 2. Fill in the proof Solve for 2x + 4 = 12 Solve for ½ x = 12

Warm Up

Statement Proof

2x + 4 = 12

2x= 8

X = 4

Statement Proof

1/2x = 12

x = 24

ImportantNext Quiz:

Friday 9/20PROOFS

Geometric Proofs

When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them.

Hypothesis Conclusion

• Definitions• Postulates• Properties• Theorems

A theorem is any statement that you can prove. Once you

have proven a theorem, you can use it as a reason in later

proofs.

Write a justification for each step, given that A

and B are supplementary and mA = 45°.

1. A and B are supplementary.mA = 45°

Given information

2. mA + mB = 180° Def. of supp s

3. 45° + mB = 180° Subst. Prop of = Steps 1, 2

4. mB = 135° Subtr. Prop of =

#1

Use the given plan to write a two-column proof.

Given: 1 and 2 are supplementary, and

1 3

Prove: 3 and 2 are supplementary.

Plan: Use the definitions of supplementary and congruent angles and substitution to show that m3 + m2 = 180°. By the definition of supplementary angles, 3 and 2 are supplementary.

#2

Example 2 Continued

Statements Reasons

1. 1.

2. 2. .

3. . 3.

4. 4.

5. 5.

1 and 2 are supplementary.

1 3

Given

m1 + m2 = 180° Def. of supp. s

m1 = m3

m3 + m2 = 180°

3 and 2 are supplementary

Def. of s

Subst.

Def. of supp. s

Write a justification for each step, given that mABC = 90° and m1 = 4m2.

1. mABC = 90° and m1 = 4m2

2. m1 + m2 = mABC

3. 4m2 + m2 = 90°

4. 5m2 = 90°

5. m2 = 18°

Given

Add. Post.

Subst.

Simplify

Div. Prop. of =.

#3

2. Use the given plan to write a two-column proof.

Given: 1, 2 , 3, 4

Prove: m1 + m2 = m1 + m4

Plan: Use the linear Pair Theorem to show that the angle pairs are supplementary. Then use the definition of supplementary and substitution.

1. 1 and 2 are supp.

1 and 4 are supp.

1. Linear Pair Thm.

2. m1 + m2 = 180°, m1 + m4 = 180°

2. Def. of supp. s

3. m1 + m2 = m1 + m4 3. Subst.

#4

CWJustification Card

Practice #1Answers

HOMEWORKANSWERS

Congruent triangles have 3 congruent sides and 3 congruent angles.

The parts of congruent triangles that “match” are called corresponding parts.

In a congruence statement

ORDER MATTERS!!!! Everything matches up.

AUG DAY

Corresponding Parts of Congruent Triangles are Congruent

Complete each congruence statement.

CA

E

D

B

F

If ABC DEF,

then BC ___

Complete each congruence statement.

CA

E

D

B

F

If ABC DEF,

then A ___

Complete each congruence statement.

CA

E

D

B

F

If ABC DEF,

then C ___F

Fill in the blanks

If CAT DOG,

then AC ___

Fill in the blanks

BAT MON

T ________ ONM_____ MONM ____

Fill in the blanks

BCA ________ GFE

Complete the congruence statement.

_____ JKN

Complete the congruence statement. _____ CBD

There are 5 ways to prove

triangles congruent.

We Use

•Sides •Angles

Side-Side-Side (SSS) Congruence Postulate

All Three sides in one triangle are congruent to all

three sides in the other triangle

Side-Angle-Side (SAS) Congruence Postulate

Two sides and the INCLUDED angle

(the angle is in between the 2 marked sides)

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT

included

Angle-Side-Angle (ASA) Congruence Postulate

Two angles and the INCLUDED side

(the side is in between the 2 marked angles)

There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES…Hypotenuse Leg

The ONLY Ways To Prove

Triangles Are Congruent

NO BAD WORDS

2 markings you can add if they aren’t marked

already

Share a side

Reason: reflexive property

Vertical Angles

Reason: Vertical Angles are congruent

Practice

1-3

Homework

Finish Triangle Congruence

Notes