Question

read explain 3b and complete your turn #1 (adapted from lesson 1.2).
perpendicular lines are lines that intersect at right angles. in the figure, line ( ell ) is
perpendicular to line ( m ). the right angle mark in the figure indicates that the lines are
perpendicular.
a ray that bisects a straight angle divides the angle into two angles
that have the same measure. in the figure, ( overrightarrow{dc} ) bisects ( angle adb ), so
( m angle a d c=m angle c d a ). the squares in the figure show the right angle
mark that indicates ( overrightarrow{d c} ) and ( overrightarrow{a b} ) are perpendicular.
( m angle a d b=m angle a d c+m angle c d a )
( m angle a d b=90^{circ}+90^{circ} )
( m angle a d b=180^{circ} )
example
(1) ( overrightarrow{c g} ) bisects segment ( overline{a b} ) at midpoint ( c ). based on the definition of angle bisector and midpoint, find the
measures of ( m angle 1 ), segment ( a c ) and ( a b ).
( m angle 1=90^{circ} )
( a c=5 )
( a b=10 )
your turn

1. ( overrightarrow{m p} ) bisects segment ( overline{l n} ) at midpoint ( m ). based on the definition of angle bisector and midpoint, find the

measures of ( m angle 1 ), segment ( l m ) and ( m n ).
( m angle 1=)
( l m=)
( m n=)

Explanation:

Step1: Find the measure of \(m\angle1\)

Since \(\overrightarrow{MP}\) is perpendicular to \(\overline{LN}\) (as per the right - angle symbol in the figure), by the definition of perpendicular lines (lines that intersect at right angles), \(m\angle1 = 90^{\circ}\)

Step2: Find the length of \(LM\) and \(MN\)

Given that \(M\) is the mid - point of \(\overline{LN}\). By the definition of a mid - point, if \(LN = 30\), then \(LM=\frac{1}{2}LN\) and \(MN=\frac{1}{2}LN\)

$$LM=\frac{1}{2}\times30 = 15$$

$$MN=\frac{1}{2}\times30=15$$

Answer:

\(m\angle1 = 90^{\circ}\), \(LM = 15\), \(MN = 15\)