Question

Complete the proof.

Given: BC = 5; AB = 3r
Prove: AB = 6

Statements Reasons
A. BC = 5 A.
B. 2x + 1 = 5 B. Substitution Property
C. 2x = 4 C.
D. x = 2 D.
E. AB = 3x E. Given
F. AB = 3(2) F.
G. AB = 6 G. Simplify

Answer 1

The question involves geometry, focusing on the proof composition method. We begin with the given information, apply substitution to find the value of 'x', and eventually prove that AB = 6 through a series of algebraic steps.

Step-by-step explanation:

The subject of this question is Mathematics, specifically, proof composition in geometry. Here is the complete proof:

1. BC = 5
   Reason: Given
2. 2x + 1 = 5
   Reason: Substitution Property (Since BC is given to equal 5, and we have the expression 2x + 1 equal to BC, we can substitute)
3. 2x = 4
   Reason: Subtraction Property of Equality (Subtracting 1 from both sides of the equation)
4. x = 2
   Reason: Division Property of Equality (Dividing both sides of the equation by 2)
5. AB = 3x
   Reason: Given
6. AB = 3(2)
   Reason: Substitution Property (Substituting the value of x into the expression for AB)
7. AB = 6
   Reason: Simplify (Multiplying 3 by 2 gives us 6)