Given : AB BC , BC DC , # # 10x 2x + 240 AB EF Prove : x 30 A B

2.7-2.8 Quiz Review KEY

Name: Honors Geometry--Stuhlman

Directions: Write a two-column proof.

1. Given bisects ; bisects ; ; and trisect ; and trisect A B C

Prove:

Q

R

D

E

S TU

Statements 1. and trisect ; and trisect 2. ; 3. 4.

5. = = =

6. + = + 7. + = ; + = 8. = 9.

Reasons 1. Given 2. Definition of Segment Trisector 3. Given 4. Two congruent segments' like divisions are congruent 5. If segments are congruent, then their measures are equal 6. Addition Property of Equality 7. Segment Addition Postulate 8. Substitution Property 9. If two segments' measures are equal, then they are congruent

2. Given: Polygon is a regular hexagon Prove: = 30

Statements 1. Polygon is a regular hexagon 2.

3. =

4. = 10; = 2 + 240 5. 10 = 2 + 240 6. 8 = 240 7. = 30

Given : AB BC, BC DC, AB EF

Prove : x 30

E 10x F

A

D 2x + 240 C

B

Reasons 1. Given 2. If a polygon is regular, all sides of the polygon are congruent 3. If two segments are congruent, then their measures are equal 4. Assumed from Diagram 5. Substitution 6. Subtraction Property (and Substitution) 7. Division Property (and Substitution)

3. Given: is the midpoint of and ; Prove: =

Given : M is the MP of BD D

C

and AC, AM MD

M

Prove : DM CM

A

B

Statements

Reasons

1. is the midpoint of and

1. Given

2.

2. Midpoint Theorem

3.

3. Given

4.

4. Transitive Property

5. =

5. If two segments are congruent, then their

measures are equal

4. Given: = ; = Prove:

Statements 1. = 2. and are vertical angles 3. 4. =

5. = 6.

2.7-2.8 Quiz Review KEY

Given: mB = mAEB,

A

C

mD = mCED

E

Prove: B D

B

D

Reasons 1. Given 2. Assumed from Diagram 3. If two angles are vertical, then they are congruent 4. If two angles are congruent, then their measures are equal 5. Transitive Property 6. If two angles' measures are equal, then they are congruent

5. Given: 3 and 4 are supplementary; 3 + 5 = 180?

Prove: 5 4

Given: 3 & 4 are supp.

m3 + m5 = 180?

Prove: 5 4

4 3

5

Statements

1. 3 + 5 = 180? 2. 3 and 5 are supplementary 3. 3 and 4 are supplementary

4. 5 4

Reasons 1. Given 2. Definition of Supplementary Angles 3. Given 4. If two angles are supplementary to the same angle, then they are congruent.

6. Given: 1 and 2 are supplementary; 2 and 3 are suppGlemiveennt:ary;1&1 2=a6r5e? supp.

Prove: 3 = 65?

2 & 3 are supp.

m 1 = 65?

1

Prove: 3 = 65?

2 3

Statements 1. 1 and 2 are supplementary; 2 and 3 are supplementary 2. 1 3

3. 1 = 3

4. 1 = 65? 5. 3 = 65?

Reasons 1. Given

2. If two angles are supplementary to the same angle, then they are congruent

3. If two angles are congruent, then their measures are equal

4. Given 5. Transitive Property of Equality

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