Rodrigo knows that am←→−⊥mn←→− and uk←→⊥mn←→− . what other facts can rodrigo conclude are true? select each correct answer.   al←→⊥lt←→   al←→∥uk←→   mn←→−∥lt←→   m∠mbk=90°

AL←→⊥LT←→

AL←→∥UK←→

MN←→−∥LT←→

m∠MBK = 90°

Parallel lines are lines that do not meet or intersect at any point.

Perpendicular lines are lines which intersect at angle 90.

Considering the diagram given in the question and the options, we can conclude that:

1. AL is perpendicular (⊥) to LT [i.e AL←→⊥LT←→] since they intersect at 90°

2. AL is parallel (∥) to UK [i.e AL←→∥UK←→] since AL and UK does not meet or intersect at any point.

3. MN is parallel (∥) to LT [i.e MN←→−∥LT←→] since MN and LT do not meet or intersect at any point

4. Angle MBK (ie m∠MBK) is 90° since it forms a right angle.

NOTE: Right angles are angles which measures exactly 90°

Therefore, all the options given in the question above are correct.

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First, let's write some definitions about lines, here we will find that the correct options are the second and fourth ones (counting from the top).

The element AM defines the line that connects points A and M, in the image, which would be the left vertical line.

The notation "AM←→−⊥MN←→"

This means that lines AM and MN are perpendiculars, which means that they intersect and form four angles of 90°.

While the notation "AL←→∥UK←→" means that the lines are parallel, so they never meet.

Now let's analyze the options to see which ones are correct:

1) " AL←→⊥LT←→"

This says that AL and LT are perpendicular, if we look at the image we can see that AL is vertical and LT is horizontal, thus, we could think that the lines are perpendicular, but we do not know for sure.

We only know that the line AM (which is the same as AL) is perpendicular to MN, but we can't conclude anything about the relation between AL and LT.

2) AL←→∥UK←→

Notice that:

AL is perpendicular to MN

UK is perpendicular to MN

We know that because its given, so both lines are perpendicular to the same line, which implies that the lines are parallel between them. So this is correct.

3) MN←→−∥LT←→

Similar to the first case, we can see that MN and LT are the two horizontal lines, but with the given information we do not know anything of LT, so we can't say that these lines are exactly parallel.

4) m∠MBK=90°

If in the intersection of two lines one of the angles has a measure of 90°, then also do the other 3 angles.

Particularly, here we can see that UBN has a measure of 90°.

Then the opposite angle of that intersection, MBK, also has a measure of 90°, then this is correct.

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