2.5 Deductive Reasoning
Geometry
1. Fill in the reason that justifies each step.
0.25x + 2x + 12 = 39
Given
2.25x + 12 = 39
a.
2.25x = 27
b.
225x = 2700
c.
x = 12
d.
2. Complete the two-column proof.
Given: m!ABC = 80!
Prove: x = 8
Statements
Reasons
1) Given
!
1) m!ABC = 80
2) m!ABD + m!DBC = m!ABC
3) (3x + 3) + (6x + 5) = 80
2) Angle Addition Postulate
3) Substitution Property
3. Complete the two-column proof.
Given: KL = 3(PM)
Prove: x = 12
Statements
Reasons
1) KL = 3(PM)
1) Given
2) 5x = 3(2x – 4)
2) Substitution Property
3) 5x = 6x – 12
3)
4) –x = -12
4)
5) x = 12
5)
4. Fill in the missing statements or reasons for the two-column proof.
Given: E is the midpoint of DF .
Prove: DE = 23
Statements
Reasons
1) E is the midpoint of DF .
1)
2)
2) Definition of midpoint
3)
3) 6x + 5 = 8x – 1
4)
4) 5 = 2x – 1
5)
5) Addition Property of Equality
6)
6) Division Property of Equality
7) Given
8)
7) DE = 6x + 5
8) DE = 6(3) + 5
9)
9) DE = 23
5. Write a two-column proof.
Given: ∠QWT and ∠TWX are complementary.
Prove: x = 28
Statements
Reasons
1) ∠QWT and ∠TWX are complementary.
1)
2) m∠QWT + m∠TWX = 90
2)
6. Write a two-column proof.
Given: KM = 35
Prove: KL = 15
Statements
Reasons