Transcript Proofs - Biancomath

Geometry Drill 9/30/10
• #1.Write a two column proof
• Given: AB=CD
• Prove: AC=BD
A
B
C
D
Put CW/HW on the corner of your desk!
Proof
Statement
Reason
1.
2.
3.
4.
1. Given
2. Reflexive property of
Equality
3. Addition Property of
Equality
4. Segment Addition
Property of Equality
5. Substitution Property
of Equality
AB=CD
BC=BC
AB +BC = CD + BC
AB +BC = AC
CD + BC = BD
5. AC = BD
Geometry Objective
• STW start connecting
information to proofs.
Geometry Theorems
• Overlapping Segments
Theorem
• Overlapping Angle Theorem
Proofs
• Example 1
• Given: mAOC  mBOD
• Prove: m1  m3
A
B
1 2
O
C
3
D
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2.
3.
4.
5.
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2.
3.
4.
5.
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2
mBOC  m2  m3
3.
4.
5.
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2 2. Angle Addition
mBOC  m2  m3
3.
4.
5.
Postulate
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2 2. Angle Addition
mBOC  m2  m3
3. m1  m2  m2  m3
4.
5.
Postulate
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2 2. Angle Addition
Postulate
3. Substitution Property
3. m1  m2  m2  m3
of Equality
mBOC  m2  m3
4.
5.
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2 2. Angle Addition
Postulate
3. Substitution Property
3. m1  m2  m2  m3
of Equality
mBOC  m2  m3
4.
5.
m2  m2
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2 2. Angle Addition
Postulate
3. Substitution Property
3. m1  m2  m2  m3
of Equality
4. m2  m2
4. Reflexive Property of
Equality
mBOC  m2  m3
5.
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2 2. Angle Addition
Postulate
3. Substitution Property
3. m1  m2  m2  m3
of Equality
4. m2  m2
4. Reflexive Property of
Equality
mBOC  m2  m3
5.
m1  m3
Proof Example 1
Statement
Reason
1. mAOC  mBOD 1. Given
2. mAOC  m1  m2 2. Angle Addition
Postulate
3. Substitution Property
3. m1  m2  m2  m3
of Equality
4. m2  m2
4. Reflexive Property of
Equality
5. Subtraction Property
5. m1  m3
of Equality
mBOC  m2  m3