Answer :
To prove that if MN- ≅ QP-, then x=7, we can use a two-column proof. If MN- is congruent to QP-, then x must equal 7.
In this two-column proof, we start with the given information that MN- is congruent to QP-. From there, we use the definitions of congruence for line segments and angles to establish that the measures of the corresponding angles are also congruent.
Statement 1: MN- ≅ QP- (Given)
Statement 2: MN ≅ QP (Definition of congruence for line segments)
Statement 3: ∠M ≅ ∠Q and ∠N ≅ ∠P (Definition of congruence for angles)
Statement 4: m∠M = m∠Q and m∠N = m∠P (Corresponding parts of congruent angles are congruent)
Statement 5: m∠M + m∠N = 180° and m∠Q + m∠P = 180° (Angles in a straight line add up to 180°)
Statement 6: m∠M + m∠N = m∠Q + m∠P (Transitive property of equality)
Statement 7: 2m∠M = 2m∠Q (Multiplication property of equality)
Statement 8: m∠M = m∠Q (Division property of equality)
Statement 9: 3x - 4 = 2x + 3 (Given that MN- = 3x - 4 and QP- = 2x + 3)
Statement 10: x = 7 (Subtracting 2x from both sides and simplifying)
Next, we use the fact that angles in a straight line add up to 180° to equate the sums of the measures of angles M and N, and angles Q and P. Using the transitive property of equality, we establish that the sums of the measures of angles M and N are equal to the sums of the measures of angles Q and P.
Now, we can proceed with the two-column proof:
As shown in the image
Therefore, we have proved that if MN- ≅ QP-, then x = 7 using a two-column proof.
Learn more about the two-column proof from the given link-
https://brainly.com/question/4769593
#SPJ11
