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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°

Rodrigo knows that AM←→⊥MN←→−and UK←→⊥MN←→−. What other facts can Rodrigo conclude-example-1

1 Answer

4 votes

Answer:


\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°

User AaronSzy
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