Two-Column Proofs

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Show your work for each problem.

1.
In a two-column proof, which reason is written next to statement 1?
1. a)Reflexive Property
2. b)Definition of supplementary angles
3. c)Substitution
4. d)Given
2.
Given: $3x + 5 = 20$ . Statement 2 uses the Subtraction Property of Equality (subtract 5 from both sides): $3x = \square$ . What number goes in the box?
3.
Given: $x + 9 = 14$ . Prove: $x = 5$ . Complete the two-column proof.
4.
Which reason justifies the statement $AB = AB$ ?
1. a)Transitive Property
2. b)Substitution
3. c)Reflexive Property
4. d)Symmetric Property
5.
Given: $\angle A$ and $\angle B$ are complementary, $m\angle A = 34^\circ$ . By the definition of complementary angles and the Subtraction Property of Equality, what is $m\angle B$ ? Write the number of degrees only.
6.
Given: $\angle 1$ and $\angle 2$ are supplementary, $m\angle 1 = 120^\circ$ . Prove: $m\angle 2 = 60^\circ$ .
7.
Statement 1: $\frac{x}{4} = 3$ (Given). Statement 2: $x = 12$ . Which reason justifies statement 2?
1. a)Distributive Property
2. b)Substitution
3. c)Multiplication Property of Equality
4. d)Division Property of Equality
8.
Given: $4(x + 3) = 36$ . Prove: $x = 6$ .
9.
Points $A$ , $B$ , $C$ lie on a line in this order. $AB = 2x + 1$ , $BC = 7$ and $AC = 20$ . Use the Segment Addition Postulate and prove the value of $x$ . What is $x$ ?
10.
$\angle 1$ and $\angle 3$ are vertical angles with $m\angle 1 = (4x + 5)^\circ$ and $m\angle 3 = 65^\circ$ . Prove: $x = 15$ .
11.
Proof: 1. $5x - 2 = 3x + 8$ (Given); 2. $2x - 2 = 8$ (Subtraction Property of Equality); 3. $2x = 10$ (?); 4. $x = 5$ (Division Property of Equality). Which reason justifies step 3?
1. a)Division Property of Equality
2. b)Addition Property of Equality
3. c)Subtraction Property of Equality
4. d)Transitive Property
12.
Given: $\frac{x}{2} - 3 = 4$ . Prove the value of $x$ using the Addition Property and then the Multiplication Property of Equality. What is $x$ ?
13.
Given: $7x - 4 = 3x + 16$ . Prove: $x = 5$ .
14.
Find the error. 1. $\frac{x}{3} + 2 = 6$ (Given); 2. $\frac{x}{3} = 4$ (Subtraction Property of Equality); 3. $x = 12$ (Division Property of Equality). Which part of the proof is wrong?
1. a)Reason 2
2. b)Statement 2
3. c)Reason 3
4. d)Statement 3
15.
$\angle 1$ and $\angle 3$ are vertical angles with $m\angle 1 = (5x - 10)^\circ$ and $m\angle 3 = (3x + 20)^\circ$ . Prove the value of $x$ , then find $m\angle 1$ . Write the number of degrees only.
16.
$\angle 1$ and $\angle 2$ form a linear pair, $m\angle 1 = (3x + 10)^\circ$ and $m\angle 2 = (2x + 20)^\circ$ . Prove: $m\angle 1 = 100^\circ$ .
17.
Points $A$ , $B$ , $C$ lie on a line in this order. $AB = x + 4$ , $BC = 2x + 5$ and $AC = 30$ . Prove: $AB = 11$ .
18.
Point $C$ lies inside the right angle $\angle ABD$ . $m\angle ABC = (2x)^\circ$ and $m\angle CBD = (3x + 15)^\circ$ . Prove: $m\angle CBD = 60^\circ$ .