Question

the segment addition postulate
find the length indicated.

1. ( h \bullet stackrel{?}{

ule{5cm}{0.15mm}} stackrel{1}{\bullet g} \bullet f )
( longleftarrow stackrel{10}{
ule{3cm}{0.15mm}} longrightarrow )

1. ( r \bullet stackrel{1}{\bullet s} stackrel{?}{

ule{5cm}{0.15mm}} \bullet t )
( longleftarrow stackrel{13}{
ule{3cm}{0.15mm}} longrightarrow )

1. ( t \bullet stackrel{?}{

ule{2cm}{0.15mm}} \bullet u stackrel{20}{
ule{3cm}{0.15mm}} \bullet v )
( longleftarrow stackrel{32}{
ule{3cm}{0.15mm}} longrightarrow )

1. ( c \bullet stackrel{14}{

ule{2cm}{0.15mm}} \bullet d stackrel{?}{
ule{2cm}{0.15mm}} \bullet e )
( longleftarrow stackrel{30}{
ule{3cm}{0.15mm}} longrightarrow )
date______

Explanation:

Problem 1

Step1: Apply Segment Addition Postulate ( \( H F = H G + G F \) )

We know \( H F = 10 \) and \( G F = 1 \). Let \( H G = x \). So \( 10 = x + 1 \).

Step2: Solve for \( x \)

Subtract 1 from both sides: \( x = 10 - 1 = 9 \).

Step1: Apply Segment Addition Postulate ( \( R T = R S + S T \) )

We know \( R T = 13 \) and \( R S = 1 \). Let \( S T = x \). So \( 13 = 1 + x \).

Step2: Solve for \( x \)

Subtract 1 from both sides: \( x = 13 - 1 = 12 \).

Step1: Apply Segment Addition Postulate ( \( T V = T U + U V \) )

We know \( T V = 32 \) and \( U V = 20 \). Let \( T U = x \). So \( 32 = x + 20 \).

Step2: Solve for \( x \)

Subtract 20 from both sides: \( x = 32 - 20 = 12 \).

Answer:

9

Problem 2