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P3 Parallel and Perpendicular: Paper 3 Challenge
P3 Parallel and Perpendicular: Paper 3 Challenge
This paper asks for reasoning: two lines perpendicular to the same line are parallel, the distance between parallel lines is constant, and two angles on a straight line add to 180 degrees, then applies these to a plumb line, a shelf and grid coordinates, and corrects the idea that the distance can change. Every item has an answer and a one-line note.
Direct answers Items 01 to 03 test recognising parallel lines, a parallelogram and a 5 cm perpendicular, 04 to 06 cover a right-angle crossing, angles on a straight line and a plumb line, 07 to 09 cover a shelf, grid coordinates and equal perpendiculars, and 10 corrects the idea of a changing distance.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P3 Parallel and Perpendicular Lines |
| Level | P3 |
02 Questions (10 items)
- FoundationIn the same plane, a is perpendicular to b and b is perpendicular to c. What is the relation between a and c?
- FoundationHow many pairs of opposite sides of a parallelogram are parallel?
- FoundationTwo parallel lines are 5 cm apart. How long is a perpendicular from a point on one line to the other?
- IntermediateTwo lines cross and one of the angles is a right angle. What are the other three?
- IntermediateAn angle and its neighbour on a straight line add to 180 degrees. If the first is 90 degrees, what is the neighbour?
- IntermediateA worker checks a wall with a plumb line. What angle should the plumb line make with the ground?
- ChallengeA shelf board must meet the side panels at a right angle so books do not slide. How many degrees is that?
- ChallengeOn grid paper, is the segment from (0,0) to (3,0) parallel or perpendicular to the segment from (1,2) to (1,5)?
- ChallengeSeveral perpendiculars are drawn between two parallel lines. One is 5 cm long; how long is another?
- Error redoCorrect this: the distance between parallel lines changes with where you measure.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | They are parallel. | Both make 90 degrees with b, so they share a direction and are parallel. |
| 2 | 2 pairs. | By definition both pairs of opposite sides of a parallelogram are parallel. |
| 3 | 5 cm. | The perpendicular between parallel lines measures the shortest distance, so it is 5 cm. |
| 4 | All 90 degrees. | Angles on a straight line add to 180 degrees, so the neighbour is 90 degrees and every angle is a right angle. |
| 5 | 90 degrees. | 180 minus 90 leaves 90, so the neighbour is 90 degrees. |
| 6 | 90 degrees. | A plumb line follows gravity and meets level ground at 90 degrees, which means the wall is truly upright. |
| 7 | 90 degrees. | A level board and an upright side panel meet at 90 degrees. |
| 8 | Perpendicular. | The first is horizontal and the second is vertical, and horizontal meets vertical at 90 degrees. |
| 9 | 5 cm. | The distance between parallel lines is the same everywhere, so each perpendicular is 5 cm. |
| 10 | Wrong. The distance between parallel lines is the same everywhere. | If the distance changed, the lines would drift together and eventually meet, so they would not be parallel. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.