Chapter 2 Proof Project 1. 2. 1. AC = BD 1. 2. AB+BC
Name: __________________________________
Chapter 2 Proof Project 1.
2.
1. AC = BD
1.
2. AB+BC = AC BC+CD = BD
2.
3. AB+BC = BC+CD
3.
4. AB + BC - BC=BC – BC + CD
4.
5. AB = CD
5.
1
Hour: _______
3.
1.
1.
2. m∠1 + m∠3 = m∠2 + m∠3
2.
3. m∠1 + m∠3 = m∠2 + m∠4
3.
4. m∠ABC = m∠1 + m∠3 m∠DEF = m∠2 + m∠4
4.
5. m∠ABC = m∠DEF
5.
4.
2
5
1. BD bisects ∠EBC
1.
2. ∠1 ≅ ∠2
2.
3. m∠1 = m∠2
3.
4. ∠2 and ∠3 form a linear pair
4.
5. ∠2 and ∠3 are supplementary
5.
6. m∠2 + m∠3 = 1800.
6.
7. m∠1 + m∠3 = 1800.
7.
8. ∠1 and ∠3 are supplementary
8.
3
6.
1. ____________________________ ____________________________
1. Given
2. ____________________________ 2. Definition of Right Angle ____________________________ 3. ____________________________ 3. Transitive Prop. Of Equality 4. ____________________________ 4. Angle Addition Postulate ____________________________ 5. ____________________________ 5. Substitution Prop.Of Equality 6. ____________________________
6. Subtraction Prop. of Equality
7. ____________________________ 7. Simplify 8. ____________________________ 8. Definition of Congruent
4
7. Given: m∠AEB = m∠CED Prove: m∠AEC = m∠DEB
1. ___________________________ 1. Given 2. ___________________________ 2. Addition Property of Equality 3. ___________________________ 3. Angle Addition Postulate ___________________________ 4. ___________________________ 4. Substitution Property of Equality
8.
Prove: 1. ___________________________ 1. Given ___________________________ 2. ___________________________ 2. Definition of Midpoint ___________________________ 3. ___________________________ 3. Trans. Prop. of Segment Cong. 4. ___________________________ 4. Definition of Congruence 5
9. Given: AB and CD bisect each other at point M. BM = CM Prove: AB = AM + DM
1._____________________________
1. Given
2._____________________________ 2. Definition of Bisect _____________________________ 3. _____________________________ 3. Definition of Congruent _____________________________ 4. ____________________________ 4. Given 5. _____________________________ 5. Transitive Prop. Of Equality 6. _____________________________ 6. Segment Addition Postulate _____________________________ 7. _____________________________ 7. Substitution P.O.E.
10.
6
11.
12.
7
13.
14.
8
Chapter 2 Proof Project 1.
2.
1. AC = BD
1.
2. AB+BC = AC BC+CD = BD
2.
3. AB+BC = BC+CD
3.
4. AB + BC - BC=BC – BC + CD
4.
5. AB = CD
5.
1
Hour: _______
3.
1.
1.
2. m∠1 + m∠3 = m∠2 + m∠3
2.
3. m∠1 + m∠3 = m∠2 + m∠4
3.
4. m∠ABC = m∠1 + m∠3 m∠DEF = m∠2 + m∠4
4.
5. m∠ABC = m∠DEF
5.
4.
2
5
1. BD bisects ∠EBC
1.
2. ∠1 ≅ ∠2
2.
3. m∠1 = m∠2
3.
4. ∠2 and ∠3 form a linear pair
4.
5. ∠2 and ∠3 are supplementary
5.
6. m∠2 + m∠3 = 1800.
6.
7. m∠1 + m∠3 = 1800.
7.
8. ∠1 and ∠3 are supplementary
8.
3
6.
1. ____________________________ ____________________________
1. Given
2. ____________________________ 2. Definition of Right Angle ____________________________ 3. ____________________________ 3. Transitive Prop. Of Equality 4. ____________________________ 4. Angle Addition Postulate ____________________________ 5. ____________________________ 5. Substitution Prop.Of Equality 6. ____________________________
6. Subtraction Prop. of Equality
7. ____________________________ 7. Simplify 8. ____________________________ 8. Definition of Congruent
4
7. Given: m∠AEB = m∠CED Prove: m∠AEC = m∠DEB
1. ___________________________ 1. Given 2. ___________________________ 2. Addition Property of Equality 3. ___________________________ 3. Angle Addition Postulate ___________________________ 4. ___________________________ 4. Substitution Property of Equality
8.
Prove: 1. ___________________________ 1. Given ___________________________ 2. ___________________________ 2. Definition of Midpoint ___________________________ 3. ___________________________ 3. Trans. Prop. of Segment Cong. 4. ___________________________ 4. Definition of Congruence 5
9. Given: AB and CD bisect each other at point M. BM = CM Prove: AB = AM + DM
1._____________________________
1. Given
2._____________________________ 2. Definition of Bisect _____________________________ 3. _____________________________ 3. Definition of Congruent _____________________________ 4. ____________________________ 4. Given 5. _____________________________ 5. Transitive Prop. Of Equality 6. _____________________________ 6. Segment Addition Postulate _____________________________ 7. _____________________________ 7. Substitution P.O.E.
10.
6
11.
12.
7
13.
14.
8
