Question

Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.A. AD¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯B. AC¯¯¯¯¯¯¯¯ || CD¯¯¯¯¯¯¯¯C. AE¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯D. none of these

Answer 1

Hi there. To solve this question, we have to remember some properties about similar triangle and congruency.

Given the triangles ADH and ECK,

We know that

`\angle ADH\cong\angle ECK`

That is, the angle at D is congruent to the angle at C in the respective triangles.

In this case, we can think of the congruency between the triangles in the following diagram:

Notice that ADCB is a parallelogram and the angles given show that the angles at D and at C are congruent, hence the other angles in the parallelogram must be congruent as well.

This means that opposite sides are parallel and have the same measure (length).

The opposite sides are AD and CB and DC and AB.

In this case, we find that only AD and CB are an option to this question, therefore the correct answer.

In fact, AC is the diagonal of the parallelogram and is not parallel to any segment of the figure.

AE isn't a segment drawn and hence not parallel to any other segment.

The correct answer is the option A).