Practice
Lines, Segments, and Rays Practice
Fifty original questions on notation, point order, opposite rays, segment addition, midpoint, segment bisectors, and algebraic lengths.
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Question 1
Explanation
A line has arrows in both directions and no endpoints.
- Reasoning
Count endpoints and arrowheads before naming the object.
Question 2
Explanation
A segment contains two endpoints and all points between them.
- Reasoning
Two solid endpoints with no arrows identify a segment.
Question 3
Explanation
A ray starts at one endpoint and extends in one direction.
- Reasoning
Look for one endpoint and one arrow.
Question 4
Explanation
The first letter in a ray name is its endpoint.
- Reasoning
Read ray notation from the endpoint toward the direction point.
Question 5
Explanation
Without a symbol above it, PQ denotes length; the bar denotes the segment object.
- Reasoning
Separate the geometric object from its numerical measure.
Question 6
Explanation
A line has no starting direction, so reversing its two point names does not change it.
- Reasoning
Only a ray uses the first letter as a directional endpoint.
Question 7
Explanation
Points contained by one straight line are collinear.
- Reasoning
Collinear refers to point placement, not angle or length relationships.
Question 8
Explanation
The rays share endpoint R and point in opposite directions along the same line.
- Reasoning
Check common endpoint, collinearity, opposite directions, and between-ness.
Question 9
Explanation
A midpoint lies on a segment and divides it into two congruent pieces.
- Reasoning
Translate midpoint directly into equal halves.
Question 10
Explanation
A segment bisector passes through the midpoint, but it need not be perpendicular.
- Reasoning
Use only the relationship encoded by the word bisector.
Question 11
Explanation
The two adjacent parts combine to form the whole segment.
- Reasoning
Read the point order as part plus part equals whole.
Question 12
Explanation
Ray ST starts at S, while ray TS starts at T.
- Reasoning
The first ray letter controls the endpoint.
Question 13
Explanation
A midpoint halves the total length: \(18/2=9\).
- Reasoning
Divide a whole segment by 2 when a midpoint is given.
Question 14
Explanation
Segment addition gives \(PR=7+11=18\).
- Reasoning
Add adjacent pieces; do not subtract unless finding a missing part.
Question 15
Explanation
Two arrowheads show continuation in both directions, which represents a line.
- Reasoning
Classify from the visible endpoint and arrow conventions.
Question 16
Explanation
The whole segment is the sum of its adjacent parts: \(6+13=19\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 17
Explanation
The whole segment is the sum of its adjacent parts: \(9+17=26\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 18
Explanation
The whole segment is the sum of its adjacent parts: \(12+5=17\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 19
Explanation
The whole segment is the sum of its adjacent parts: \(14+19=33\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 20
Explanation
The whole segment is the sum of its adjacent parts: \(8+23=31\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 21
Explanation
The whole segment is the sum of its adjacent parts: \(16+11=27\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 22
Explanation
The whole segment is the sum of its adjacent parts: \(21+7=28\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 23
Explanation
The whole segment is the sum of its adjacent parts: \(18+25=43\).
- Reasoning
Write \(PQ+QR=PR\) before substituting.
Question 24
Explanation
A midpoint creates equal halves, so \(AB=AM+MB=8+8=16\).
- Reasoning
Double one half to obtain the whole segment.
Question 25
Explanation
A midpoint creates equal halves, so \(AB=AM+MB=11+11=22\).
- Reasoning
Double one half to obtain the whole segment.
Question 26
Explanation
A midpoint creates equal halves, so \(AB=AM+MB=14+14=28\).
- Reasoning
Double one half to obtain the whole segment.
Question 27
Explanation
A midpoint creates equal halves, so \(AB=AM+MB=17+17=34\).
- Reasoning
Double one half to obtain the whole segment.
Question 28
Explanation
A midpoint creates equal halves, so \(AB=AM+MB=22+22=44\).
- Reasoning
Double one half to obtain the whole segment.
Question 29
Explanation
A midpoint creates equal halves, so \(AB=AM+MB=26+26=52\).
- Reasoning
Double one half to obtain the whole segment.
Question 30
Explanation
A midpoint creates equal halves, so \(AB=AM+MB=31+31=62\).
- Reasoning
Double one half to obtain the whole segment.
Question 31
Explanation
Midpoint halves are equal. Solving the two expressions gives \(x=5\); each half is 23, so the whole is 46.
- Reasoning
Set the two half expressions equal, evaluate one half, then double it.
Question 32
Explanation
Midpoint halves are equal. Solving the two expressions gives \(x=7\); each half is 37, so the whole is 74.
- Reasoning
Set the two half expressions equal, evaluate one half, then double it.
Question 33
Explanation
Midpoint halves are equal. Solving the two expressions gives \(x=6\); each half is 41, so the whole is 82.
- Reasoning
Set the two half expressions equal, evaluate one half, then double it.
Question 34
Explanation
Midpoint halves are equal. Solving the two expressions gives \(x=8\); each half is 43, so the whole is 86.
- Reasoning
Set the two half expressions equal, evaluate one half, then double it.
Question 35
Explanation
Midpoint halves are equal. Solving the two expressions gives \(x=9\); each half is 67, so the whole is 134.
- Reasoning
Set the two half expressions equal, evaluate one half, then double it.
Question 36
Explanation
Midpoint halves are equal. Solving the two expressions gives \(x=10\); each half is 87, so the whole is 174.
- Reasoning
Set the two half expressions equal, evaluate one half, then double it.
Question 37
Explanation
The bisector passes through midpoint N, so \(JN=NK=24\) and \(JK=48\).
- Reasoning
Translate segment bisector to midpoint equality, then double.
Question 38
Explanation
Because B is between A and C, \(AB+BC=AC\), so \(BC=34-19=15\).
- Reasoning
Subtract the known part from the whole.
Question 39
Explanation
Opposite rays require a common endpoint, collinearity, opposite directions, and the common endpoint between the outer points.
- Reasoning
Test every condition in the definition.
Question 40
Explanation
The midpoint guarantees equal halves; perpendicularity is not implied.
- Reasoning
Infer only relationships that are marked or stated.
Question 41
Explanation
Add every nonoverlapping consecutive part: \(5+9+12=26\).
- Reasoning
Trace the whole from the first endpoint to the last and include each piece once.
Question 42
Explanation
Add every nonoverlapping consecutive part: \(8+14+7=29\).
- Reasoning
Trace the whole from the first endpoint to the last and include each piece once.
Question 43
Explanation
Add every nonoverlapping consecutive part: \(11+6+18=35\).
- Reasoning
Trace the whole from the first endpoint to the last and include each piece once.
Question 44
Explanation
The ratio has 8 total parts, so each part is 8; \(PM=3(8)=24\).
- Reasoning
Convert the ratio to total equal parts before assigning lengths.
Question 45
Explanation
Let \(QR=x\). Then \((2x+3)+x=39\), so \(3x=36\) and \(x=12\).
- Reasoning
Express both parts with one variable and set their sum equal to the whole.
Question 46
Explanation
Since \(PR=2PM\), \(10x-32=8x-14\), so \(x=9\). Therefore \(MR=PM=4(9)-7=29\).
- Reasoning
Set the whole equal to twice the half, then evaluate the half.
Question 47
Explanation
Ray YX starts at Y and points left; ray YZ shares endpoint Y and points right.
- Reasoning
Locate the common endpoint first, then choose a point on the opposite side.
Question 48
Explanation
A segment bisector need not form a right angle unless perpendicularity is separately marked or stated.
- Reasoning
Separate the two meanings: bisects versus perpendicular.
Question 49
Explanation
First \(BC=BD-CD=17\). Then \(AC=AB+BC=7+17=24\).
- Reasoning
Use the overlapping whole BD to recover BC before building AC.
Question 50
Explanation
The half \(PM=PQ+QM=13\). Since M is midpoint, \(PR=2(13)=26\).
- Reasoning
Build one half first, then use the midpoint to double.
Keyboard: use Tab to move, arrow keys to change answer choices, and Enter to check an answer.
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Questions to review
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- Question 1Line, segment, and ray definitionsEasy
- Question 2Line, segment, and ray definitionsEasy
- Question 3Line, segment, and ray definitionsEasy
- Question 4Ray notationEasy
- Question 5Segment notationEasy
- Question 6Notation and orderEasy
- Question 7Collinear pointsEasy
- Question 8Opposite raysEasy
- Question 9Midpoint definitionEasy
- Question 10Segment bisectorEasy
- Question 11Segment Addition PostulateEasy
- Question 12Ray notationEasy
- Question 13Midpoint calculationEasy
- Question 14Segment Addition PostulateEasy
- Question 15Diagram interpretationEasy
- Question 16Segment additionMedium
- Question 17Segment additionMedium
- Question 18Segment additionMedium
- Question 19Segment additionMedium
- Question 20Segment additionMedium
- Question 21Segment additionMedium
- Question 22Segment additionMedium
- Question 23Segment additionMedium
- Question 24Midpoint calculationMedium
- Question 25Midpoint calculationMedium
- Question 26Midpoint calculationMedium
- Question 27Midpoint calculationMedium
- Question 28Midpoint calculationMedium
- Question 29Midpoint calculationMedium
- Question 30Midpoint calculationMedium
- Question 31Algebraic midpointMedium
- Question 32Algebraic midpointMedium
- Question 33Algebraic midpointMedium
- Question 34Algebraic midpointMedium
- Question 35Algebraic midpointMedium
- Question 36Algebraic midpointMedium
- Question 37Segment bisector calculationMedium
- Question 38Missing segment partMedium
- Question 39Opposite-ray reasoningMedium
- Question 40Segment-bisector reasoningMedium
- Question 41Multi-segment additionHard
- Question 42Multi-segment additionHard
- Question 43Multi-segment additionHard
- Question 44Segment ratiosHard
- Question 45Algebraic segment additionHard
- Question 46Algebraic midpointHard
- Question 47Opposite raysHard
- Question 48Error analysisHard
- Question 49Overlapping segmentsHard
- Question 50Multi-step midpointHard