Unit 1: Geometry Basics Homework 2: Segment Addition Postulate
- If LM= 22 and MN = 15, find LN.
- If LN = 54 and LM = 31, find MN.
- If DF = 9x – 39, find EF.
- 3x + 10
The correct answer and explanation is:
Homework 2: Segment Addition Postulate
The Segment Addition Postulate states that if a point B is between A and C, then: AB+BC=ACAB + BC = AC
We’ll use this principle to solve the given problems.
Solutions:
- If LM = 22 and MN = 15, find LN. LN=LM+MNLN = LM + MN LN=22+15=37LN = 22 + 15 = 37
- If LN = 54 and LM = 31, find MN. MN=LN−LMMN = LN – LM MN=54−31=23MN = 54 – 31 = 23
- If DF = 9x – 39, find EF.
We need more information to determine EF. If you have values for other segments, please provide them. - Given 3x+103x + 10, find the correct answer and provide a 300-word explanation.
Explanation of the Segment Addition Postulate (300 Words)
The Segment Addition Postulate is a fundamental concept in geometry that states that if a point lies between two other points on a line segment, the sum of the two smaller segments equals the total length of the segment.
For example, if we have three points A, B, and C on a line where B is between A and C, then: AB+BC=ACAB + BC = AC
This postulate is useful when solving problems related to line segments and their lengths. By knowing two segments, we can determine the missing third segment by simple addition or subtraction.
Let’s analyze the given problems:
- In Problem 1, since L, M, and N lie on a straight line, adding LM and MN gives the full length LN.
- In Problem 2, knowing the total length LN and part of it (LM), we find the missing segment (MN) by subtracting LM from LN.
- Problem 3 requires more details, as we are given an algebraic expression for DF but not enough information about EF.
- Problem 4 involves an algebraic expression 3x + 10, which may represent a segment’s length. If we substitute a given value for x, we can compute its numerical length.
The Segment Addition Postulate is frequently used in coordinate geometry, algebra, and proofs. It helps us determine missing lengths and serves as a foundation for more complex theorems, such as the midpoint formula and bisectors. Understanding this concept is crucial for solving problems involving line segments, distances, and algebraic expressions in geometry.
Now, let me generate an image illustrating the Segment Addition Postulate.
Here is the geometric diagram illustrating the Segment Addition Postulate with points L, M, and N and their respective segment lengths. Let me know if you need any modifications!
