Question: User: Name: Brady Hicm
Date: 8/26/26 Per: 5th
Unit 1: Geometry Basics
Homework 2: Segment Addition Postulate
** This is a 2-page document! **
Use the diagram below to
answer questions 1 and 2.
L M N
1. If $LM = 22$ and $MN = 15$, find $LN$.
2. If $LN = 54$ and $LM = 31$, find $MN$.
3. If $RT = 36$, find the value of $x$.
R S T
$6x + 1$ $x + 7$
4. If $DF = 9x - 39$, find $EF$.
D E F
$47$ $3x + 10$
5. If $UW = 6x - 35$, find $UW$.
U V W
$19$ $4x - 20$
6. If $HJ = 7x - 27$, find the value of $x$.
H I J
$3x - 5$ $x - 1$
1. **Problem:** Given points $L$, $M$, and $N$ on a line segment with $LM = 22$ and $MN = 15$, find $LN$.
2. **Formula:** The Segment Addition Postulate states that if $M$ is between $L$ and $N$, then:
$$LN = LM + MN$$
3. **Calculation:** Substitute the given values:
$$LN = 22 + 15$$
$$LN = 37$$
4. **Answer:** The length of segment $LN$ is $37$.
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1. **Problem:** Given $LN = 54$ and $LM = 31$, find $MN$.
2. **Formula:** Using the Segment Addition Postulate:
$$LN = LM + MN$$
3. **Calculation:** Rearrange to find $MN$:
$$MN = LN - LM$$
$$MN = 54 - 31$$
$$MN = 23$$
4. **Answer:** The length of segment $MN$ is $23$.