Question

M

L
K
Complete the two-column proof by filling in the blanks.
Given: MJ = KL, ZMLJ and ZKJL are right angles.
Prove: AMLJ=A KIL
Statements
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1.
MJ KL, ZMLJ and ZKJL are right angles.
4. U=U
1.
5. AMLA KIL
2.
2.
ZMLJ and ZKJL are right angles. [Select]
3.
3.
AML and AKIL are right triangles. [Select]
[Select]
4.
5.
[ Select]
J
[Select]
Reason

Answer 1

To prove that triangles AMLJ and AKIL are congruent, the two-column proof uses the given congruent sides and the property of right angles, concluding with the Hypotenuse-Leg (HL) Theorem.

Step-by-step explanation:

To complete the two-column proof for the question given that MJ = KL, and ∠MLJ and ∠KJL are right angles, thus proving that triangles AMLJ and AKIL are congruent:

1. Given: MJ = KL, ∠MLJ and ∠KJL are right angles.
2. ∠MLJ and ∠KJL are right angles. Reason: Given.
3. Triangles AML and AKIL are right triangles. Reason: Definition of a right triangle.
4. MJ = KL. Reason: Given.
5. Triangles AMLJ and AKIL are congruent. Reason: Hypotenuse-Leg (HL) Theorem.

The proof relies primarily on the fact that we have two right triangles with one congruent side and one right angle each, which allows us to conclude congruence by the HL theorem.