Question

use the figures to determine whether the indicated lines are para

a) figure: horizontal lines ( m ), ( n ); transversal ( p ) with ( 144^circ ) (above ( m )) and ( 36^circ ) (below ( n ))

b) figure: horizontal lines ( q ), ( r ); transversal ( p ) (vertical) with ( 97^circ ) (above ( q )) and ( 83^circ ) (below ( r ))

c) partially visible

d) are ( u ) and ( v ) parallel lines? why or why not?
a. no, because adjacent angles are not supplementary
b. no, because alternate exterior angles are not equal
c. yes, because corresponding angles are ( 90^circ ) each
d. yes, because vertical angles are complementary

e) figure: horizontal lines ( y ), ( z ); transversal ( p ) (diagonal) with ( 155^circ ) (above ( y )) and ( 155^circ ) (below ( z ))

f) partially visible

Explanation:

To determine if lines \( u \) and \( v \) are parallel, we analyze the angles formed by the transversal \( p \).

Step 1: Identify the angle relationship

The transversal \( p \) forms angles with lines \( u \) and \( v \). Both angles are right angles ( \( 90^\circ \) ), which are corresponding angles.

Step 2: Apply the Corresponding Angles Postulate

The Corresponding Angles Postulate states that if corresponding angles are equal, then the lines are parallel. Since both corresponding angles are \( 90^\circ \), they are equal.

Answer:

C. Yes, because corresponding angles are \( 90^\circ \) each