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Quizzes > High School Quizzes > Mathematics

Using the Segment Addition Postulate Practice Quiz

Sharpen geometry skills with real practice tests

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting a Segment Addition Fact Check quiz for middle school students.

What does the segment addition postulate state?
The sum of any two segments is always greater than the third.
If point B is between points A and C, then AB + BC = AC.
Segments can only be added when they are perpendicular.
The product of two segment lengths equals the total length.
The segment addition postulate states that when a point lies between two others on a line, the sum of the lengths of the two smaller segments equals the length of the entire segment. This is a fundamental concept in geometry.
If point B is between A and C, and AB = 3 and BC = 4, what is AC?
1
0
7
12
By the segment addition postulate, AC is the sum of AB and BC. Therefore, 3 + 4 equals 7.
Which of the following best exemplifies the segment addition postulate?
Subtracting one segment from another to find a difference.
Adding the lengths of two adjacent segments on a straight line to get the total length.
Multiplying two segment lengths to obtain an area.
Dividing a segment into equal parts.
The postulate is demonstrated by the addition of adjacent segment lengths along the same line to find the total length. This concept is important for solving many geometric problems.
For collinear points A, B, and C, if AB = 2 cm and BC = 5 cm, what is AC?
None of the above
3 cm
10 cm
7 cm
Using the segment addition postulate, AC is found by adding AB and BC, resulting in 2 cm + 5 cm = 7 cm.
What condition is necessary for the segment addition postulate to be applicable?
The points must form a triangle.
The segments must be perpendicular.
The points must be collinear with the middle point between the endpoints.
The segments must be equal in length.
The postulate applies only when the points lie on the same straight line with one point located between the other two. This condition is essential to ensure accurate addition of segment lengths.
In a line segment AC, if AB is 9 and AC is 15, what is the length of BC?
8
6
4
24
Using the postulate AB + BC = AC, subtract AB from AC to find BC: 15 - 9 equals 6.
In triangle ABC, if D lies on side AC, which equation correctly represents the segment addition postulate for side AC?
AD - DC = AC
AD + DC = AC
AD / DC = AC
AD x DC = AC
The segment addition postulate tells us that the two parts of a segment, AD and DC, when added together, equal the entire segment AC.
Point B lies between A and C. If AB = x, BC = 7, and AC = 12, what is the value of x?
12
0
5
7
The segment addition postulate gives the equation x + 7 = 12. Solving, x is equal to 5.
If segment MN is divided by point P such that MP = 4 and PN = 6, what is the total length of MN?
24
6
10
2
According to the segment addition postulate, MN is found by adding the lengths of MP and PN: 4 + 6 equals 10.
Which condition must be met for the segment addition postulate to be valid?
The points must be collinear with the middle point between the endpoints.
All segments must be parallel.
The segments must be equal.
The segments must be perpendicular.
For the postulate to apply, the points involved must lie on the same straight line with one point specifically between the other two, ensuring proper addition of segment lengths.
If DE + EF = DF and DE is 3/5 of DF, what fraction of DF is EF?
1/2
2/5
3/5
1/3
Since DE is 3/5 of DF, the remainder, EF, must equal DF - 3/5 DF, which is 2/5 of DF.
A student claims that if AB = 4 and BC = 5, then AC must be 10. What is the error in this claim?
The student subtracted the segments instead of adding them.
The student incorrectly added the segments; 4 + 5 is actually 9.
The student should multiply the segments.
There is no error because 4 + 5 equals 10.
The correct method is to add the segment lengths, yielding 4 + 5 = 9. The student's error was in basic addition.
For collinear points G, H, and I, if GH = 6, HI = k, and GI = 10, what is the value of k?
4
16
10
6
Since GH + HI = GI, substituting gives 6 + k = 10, which means k must be 4.
If the segment addition postulate holds for points A, B, and C with AB = 7 and AC = 12, what is the length of BC?
19
7
12
5
Using the postulate, BC is obtained by subtracting AB from AC: 12 - 7 equals 5.
How does the segment addition postulate assist in solving geometric problems?
It breaks down complex shapes into circles.
It calculates the area of a polygon.
It determines angles between intersecting lines.
It allows the determination of an unknown segment length by adding known adjacent segments.
The postulate is critical in finding unknown lengths along a line through the addition of adjacent segments. This technique is widely used in various geometric problems.
In a line segment XY, point Z divides XY in the ratio 3:2. If XY = 25, what is the measure of XZ?
18
10
15
12
Since point Z divides XY in a 3:2 ratio, XZ is 3/5 of the entire segment, so 3/5 of 25 is 15.
Three collinear points A, B, and C satisfy AB = 2x, BC = x + 3, and AC = 5. Solve for x.
1
2
2/3
3
Applying the postulate, 2x + (x + 3) = 5, which simplifies to 3x + 3 = 5, so x = (5 - 3) / 3 = 2/3.
Line segment LM is divided by point N. If LM = 3k + 2 and LN = 2k - 1, what is the expression for NM?
2k + 3
k - 3
k + 3
5k + 1
Using the segment addition postulate, NM is the difference between LM and LN, which simplifies to (3k + 2) - (2k - 1) = k + 3.
On a number line, point A is at 1, B is at m, and C is at 9. If m = 4, what is the measure of segment AB?
3
8
5
4
Since AB is the difference between m and 1, substituting m = 4 gives AB = 4 - 1, which is 3.
Points P, Q, and R are collinear. Given that PQ = x + 2, QR = 2x - 1, and PR = 14, find x.
5
3
13/3
4
By the postulate, (x + 2) + (2x - 1) = 14, which simplifies to 3x + 1 = 14. Solving gives x = (14 - 1) / 3 = 13/3.
0
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Study Outcomes

  1. Understand the segment addition postulate and its applications in middle school geometry.
  2. Apply the segment addition postulate to determine unknown segment lengths.
  3. Analyze interactive questions to identify key elements of the segment addition concept.
  4. Evaluate the validity of given geometric statements using the segment addition postulate.
  5. Synthesize information from quiz problems to prepare effectively for exam scenarios.

Segment Addition Postulate Cheat Sheet

  1. Understand the Segment Addition Postulate - Ever wondered how to break up a line like a pro? If points A, B, and C are collinear with B in between, then AB + BC equals AC. This rule will be your go‑to for basic segment calculations! splashlearn.com
  2. Set Up Equations for Unknown Segments - When you see algebraic expressions for segment lengths, channel your inner sleuth and write equations based on AB + BC = AC. Solving these equations lets you unmask missing lengths in a flash. Practice a few and you'll notice your equations practically solve themselves! chilimath.com
  3. Link with Segment Congruence - The postulate isn't just math trivia; it's a vital tool for proving when segments are congruent and collinear. By showing AB + BC = AC, you confirm points lie on the same line and that segments line up just right. Master this connection and congruence proofs become a breeze! wikipedia.org
  4. Determine If a Point Lies Between Others - Wonder if a point sits in the middle of two others? Check if the sum of the smaller segments matches the total length. When it does, you've got a "between" situation on your hands - no guesswork needed! allmathwords.org
  5. Solve Algebraic Segment Problems - Algebra meets geometry when segment lengths sport variables. Set up your AB + BC = AC equation, solve for the variable, and boom - you've got the segment's exact measure. It's like cracking a mini math code! basic-mathematics.com
  6. Stick to Collinear Points Only - Here's a golden rule: the postulate only works when points lie flat on the same line. If they don't, the rule falls apart. Keeping an eye on collinearity will save you from wild goose chases! splashlearn.com
  7. Extend to Multiple Collinear Points - What if more than three points line up? No problem - just keep adding segments like AB + BC + CD = AD and so on. This extended approach helps you tackle complex line setups without breaking a sweat! splashlearn.com
  8. Connect with the Triangle Inequality - Peek into the triangle inequality: any two sides of a triangle summed are always longer than the third side. This concept builds on the idea of adding segments and guarding against shortcuts that fail in triangles. Adding this into your toolkit sharpens both postulate and triangle skills! wikipedia.org
  9. Find Midpoints Using the Postulate - Midpoints are all about equal halves! If AB + BC = AC and AB equals BC, you've pinpointed the exact midpoint at B. This trick is perfect for bisecting segments in geometric constructions. splashlearn.com
  10. Apply It in Real‑World Contexts - From measuring garden plots to crafting accurate blueprints, this postulate is a real-life hero. Use it to verify distances, plan layouts, and ensure precision in your next project. Who knew learning geometry could make everyday tasks easier? cuemath.com
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