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3.06 Module Three Activity

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by

Annie Maroon

on 12 December 2013

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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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