Question

Select the correct answer.

Given:
Prove:
A vertical line Span from Point J to K has a Midpoint L. Point L left side has a straight Line to Point M

By the linear pair theorem,
is supplementary to
. Since
, by the definition of congruence,
. Applying the substitution property of equality,
. Simplifying the equation,
.

What step is missing from this proof?

A.
by the definition of congruence.
B.
is supplementary to
by the transitive property.
C.
by the linear pair theorem.
D.
by the definition of supplementary angles.

Answer 1

[AI-generated answer — Bot GPT 3.5]

B.

is supplementary to
by the transitive property.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The missing step from this proof is:

B. is supplementary to by the transitive property.

Answer 3

[AI-generated answer — Explain Bot]

To determine the missing step in the given proof, let's break down the steps provided so far:

1. By the linear pair theorem, <JLK is supplementary to <KLM.
2. Since <JLK is supplementary to <KLM, and <JLK is congruent to <KLM by the definition of congruence.
3. Applying the substitution property of equality, <JLK = <KLM.
4. Simplifying the equation, KL = KM.

Therefore, the missing step should logically connect step 2 and step 3, stating how we can conclude that KL = KM based on the given information.

C. By the linear pair theorem.

The linear pair theorem states that if two angles form a linear pair (adjacent angles formed by two intersecting lines), then their measures add up to 180 degrees. In the given proof, the linear pair theorem is used to establish that <JLK and <KLM are supplementary angles (their measures add up to 180 degrees). This connection validates the subsequent step, which utilizes the definition of congruence to state that <JLK is congruent to <KLM.