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More Proofs Practice Ch.2
Honors Geometry
1)
Name_______Key________________
Given: ABC is a right angle
m2  m3
Prove: m1  m3  90
Statements
Reasons
1. ABC is a right angle
1. Given
2. m<ABC = 90
2. Def. of Right Angle
3. mABC  m1  m2
3. Angle Addition Postulate
4. 90 = m<1 + m<2
4. Substitution
5. m<2 = m<3
5. Given
6. m<1 + m<3 = 90
6. Substitution
2)
Given: 1 and 2 form a linear pair
m2  m3  m4  180
Prove: m1  m3  m4
Statements
Reasons
1. 1 and 2 form a linear pair
1. Given
2. <1 and <2 are supplementary
2. Linear Pair Theorem
3. m<1 + m<2 = 180
3. Definition of Supplementary Angles
4. m<2 + m<3+m<4 = 180
4. Given
5. m1  m2  m2  m3  m4
5. Transitive/Substitution
6. m<1 = m<3 + m<4
6. Subtraction
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3)
Given: mHGK  mJGL
Prove: m1  m3
Statements
Reasons
1. m<HGK = m<JGL
1. Given
2. m<HGK = m<1 + m<2
2. Angle Addition Postulate
3. m<JGL = m<2+m<3
3. Angle Addition Postulate
4. m1  m2  m2  m3
4. Transitive/Substitution
5. m<1 = m<3
5. Subtraction
4)
Given: ABC  EFG
1  3
Prove: 2  4
Statements
Reasons
1. ABC  EFG
1.Given
2. m<ABC = m<EFG
2. Def. of Congruent Angles
3. mABC  m1  m2
3. Angle Addition Postulate
4. mEFG  m3  m4
4. Angle Addition Postulate
5. m<1 +m<2 = m<3+m<4
5. Transitive Property
6. 1  3
6. Given
7. m<1 = m<3
7. Def. of Congruent Angles
8. m2  m4
8. Subtraction
9. 2  4
9. Def. of Congruent Angles
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5)
Given: m1  m3
m2  m4
Prove: mABC  mADC
Statements
Reasons
1. m1  m3
1. Given
2. m2  m4
2. Given
3. m1  m2  m3  m4
3. Addition
4. m<1+m<2 = m<ABC
4. Angle Addition Postulate
5. m<3+m<4 = m<ADC
5. Angle Addition Postulate
6. mABC  mADC
6. Transitive/Substitution
6)
Given: PT  QT
TR  TS
Prove: PR  QS
Statements
Reasons
1. PT  QT
1. Given
2. PT=QT
2. Def. of Congruent Segments
3. TR  TS
3. Given
4. TR = TS
4. Def. of Congruent Segments
5. PT+TR = QT+TS
5. Addition Property
6. PT + TR = PR
6. Segment Addition Postulate
7. QT + TS = QS
7. Segment Addition Postulate
8. PR=QS
8. Transitive/Substitution
9. PR  QS
9. Def. of Congruent Segments
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