Question

For lines c, d and e, m1 = 90° and m3=90°



For the given diagram and angle measures, use complete sentences to describe each pair of lines as parallel or perpendicular. In your description, include the special angle relationship between angles 1 and 3.


lines d and e
lines d and c
For lines c, d and e, m1 = 90° and m3=90°



For the given diagram and angle measures, use complete sentences to describe each pair of lines as parallel or perpendicular. In your description, include the special angle relationship between angles 1 and 3.


lines d and e
lines d and c

Answer 1

Given :  lines c, d and e, m∠1 = 90° and m∠3=90°

To Find : describe each pair of lines as parallel or perpendicular

lines d and e

lines d and c

Solution:

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent.  

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Interior angles are supplementary. ( adds up to 180°)

Perpendicular lines has 90° angle between them

m∠1 = 90°    

∠1  is between d & c

Hence d & c are perpendicular lines

m∠1 = m∠3=90°

Corresponding angles are congruent.

Hence lines d and e are parallel   ( c is transversal )

Perpendicular lines has 90° angle between them

m∠3 = 90°    

∠3  is between e & c

Hence e & c are perpendicular lines

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