Take Note: Theorem 3-9 Perpendicular Transversal Theorem

Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.

If …

n ⊥ l n up tack l  and l || m l vertical linevertical line m

Then …

n ⊥ m n up tack m

You will prove Theorem 3-9 in Exercise 10.

Proof: Problem 2 Proving a Relationship Between Two Lines

Given: In a plane, c ⊥ b , b ⊥ d , c up tack b comma b up tack d comma  and d ⊥ a . d up tack eh .

Prove: c ⊥ a c up tack eh

Proof: Lines c and d are both perpendicular to line b, so c || d c vertical linevertical line d  because two lines perpendicular to the same line are parallel. It is given that d ⊥ a . d up tack eh .  Therefore, c ⊥ a c up tack eh  because a line that is perpendicular to one of two parallel lines is also perpendicular to the other (Perpendicular Transversal Theorem).

✓ Got It?

2. In Problem 2, could you also conclude a || b ? eh vertical linevertical line b question mark  Explain.