#### Transcript of 3.06 Module Three Activity

**3.06 Module Three Activity**

Line/Angle Proof:

Alternate Interior Angles

Given:

A || B, <3 congruent to <2

Prove:

<3 congruent to <6

Two column proof:

1.

AB || CD = Given

2.

<3 congruent to <2 = Given

3.

<3 congruent to <2 = Vertical Angle Theorem

4.

<2 congruent to <6 = Corresponding Angles Theorem Postulate

5.

<3 congruent <6 =Transitive Property

Triangle Proof:

Isosceles Triangle

Given:

DE congruent to EF

Prove:

<D congruent to <F

Two column proof:

1.

DE congruent to EF= Given

2.

Draw EG = Construction of perpendicular bisector

3.

<DEG congruent to <FEG = Definition of perpendicular bisector

4

. EG congruent to EG = Reflexive Property of Equality

5

.Triangle EDG congruent to Triangle EFD = SAS

6

. <D congruent <F = CPCTC

Parallelogram Proof:

Opposite Angles are Congruent

Given:

Quadrilateral ABCD is a parallelogram

Proof:

<A congruent to <D and <B congruent to <C

Two column proof:

1.

ABCD is a parallelogram = given

2.

AC || BD, CD || AB = Definition of parallelogram

3.

Extend each side of the parallelogram and place a point on each extension = By Construction

4.

<CAB congruent <GCA = Alternate Interior Angles Theorem

5.

<GCA Congruent to <BDC = Corresponding Angles Theorem

6.

<CAB congruent to < BDC = Transitive Property of Equality

7.

<ACD congruent to <CDI = Alternate Interior Angles Theorem

8

. <CDI congruent to <DBA = Corresponding Angles Theorem

9.

<ACD congruent to <DBA = Transitive Property of Equality

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