Question

If JKLM is a trapezoid, which statements must be true? Check all that apply.

Answer 1

Answer:

Options A and E are correct choices.

Step-by-step explanation:

We have been given diagram of a trapezoid. We are asked to choose the correct option about our given trapezoid.  

We will use trapezoid properties to solve our given problem.  

We know that each lower base angle is supplementary to the upper base angle on the same side.  

We can see that angle K is upper base angle and angle J is lower base angle, so $\angle J$ is supplementary to angle $\angle K$. Therefore, option A is the correct choice.

If we have been given that our given trapezoid is an isosceles trapezoid, then angle J must be congruent to angle M as lower base angles of an isosceles trapezoid are congruent. Since we have not been given that our given trapezoid is an isosceles trapezoid, therefore, we cannot choose option B.

We know that bases of a trapezoid are parallel by definition.

Upon looking at our given diagram, we can see that segment KL and segment JM are bases, so line segment KL must be parallel to line segment JM. Therefore, option E is the correct choice.

Answer 2

A trapezoid has a pair of parallel sides and non-parallel sides.

The true statements are:

• (a) J is supplementary to K
• (e) KL is parallel to JM

The angles at the adjacent points of a trapezoid add up to 180 degrees

This means that:

• $J + K = 180$ --- supplementary angles
• $L + M = 180$ --- supplementary angles

The above highlights mean that: J and K are supplementary angles

Hence, (a) is true

Also, a trapezoid has a pair of parallel sides

Because lines KL and JM are horizontal lines, then they must be parallel to one another.

The above highlight means that: Lines KL and JM are parallel lines.

Hence, (e) is true

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