Question

Rodrigo knows that AM←→⊥MN←→−and UK←→⊥MN←→−.

What other facts can Rodrigo conclude are true?



Select each correct answer.

AL←→⊥LT←→
line A L is perpendicular to line L T

AL←→∥UK←→
line A L is parallel to line U K

MN←→−∥LT←→
line M N is parallel to line L T

m∠MBK=90°

Answer 1

`\overleftrightarrow{AL} \parallel \overleftrightarrow{UK} \ \ \huge \checkmark`

`m\angle MBK=90^(\circ )\ \huge \checkmark`

Explanation:

We are given :

`\overleftrightarrow{AM} \perp \overleftrightarrow{MN}`

and

`\overleftrightarrow{UK} \perp \overleftrightarrow{MN}`

………………………………………………

The lines AM and UK are perpendicular to the same line MN.

Then

`\overleftrightarrow{AM} \parallel \overleftrightarrow{UK}`

We also have :

`\overleftrightarrow{AM} = \overleftrightarrow{AL}`

Therefore ,

`\overleftrightarrow{AL} \parallel \overleftrightarrow{UK}`

………………………………………………………

∠MBK and ∠UBN are two vertically opposite angles.

Then

m∠MBK = m∠UBN

Since , m∠UBN = 90°

Then

m∠MBK = 90°