中文（繁體）
中文（简体）
English
P3 Parallel and Perpendicular: Paper 4 Error Clinic
P3 Parallel and Perpendicular: Paper 4 Error Clinic
This paper targets common slips: two misconceptions about parallel and perpendicular lines, then parallel pairs in a rectangle, the four right angles of a square, right angles at a crossing, adjacent angles on a straight line and equal gaps between parallel lines, and finally two lines perpendicular to a third and directions on squared paper. Every item has an answer and a one-line note.
Direct answers Items 01 to 03 fix the not-touching slip and count parallel pairs and right angles, 04 to 06 cover four right angles at a crossing, adjacent angles and equal gaps, 07 to 09 are a third-line argument, rectangle sides and grid directions, and 10 corrects the equal-length slip.
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)
- FoundationCorrect this: two lines that do not touch are parallel.
- FoundationA rectangle has 4 sides. How many pairs of parallel opposite sides are there?
- FoundationEach corner of a square is 90 degrees. How many degrees are the four corners altogether?
- IntermediateWhen two lines cross at right angles, how many right angles form at the crossing?
- IntermediateTwo adjacent angles on a straight line add up to 180 degrees. If one is 65 degrees, what is the other?
- IntermediateTwo parallel lines are 4 cm apart. Measured from two different points on one line, what distance do you get each time?
- ChallengeLine a is perpendicular to b, and b is perpendicular to c. Are a and c parallel or perpendicular?
- ChallengeA rectangle is 12 cm by 5 cm and every corner is a right angle. At what angle do the long and short sides meet?
- ChallengeOn squared paper, AB runs from (0,0) to (4,0) and CD from (2,1) to (2,5). Are AB and CD parallel or perpendicular?
- Error redoCorrect this: if two lines are perpendicular, they must be the same length.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Not exactly. Parallel lines lie in the same plane and never meet even when extended forever. | Not touching on the page is not enough: the lines may meet once extended, so extend them before you decide. |
| 2 | 2 pairs. | The top and bottom form one parallel pair and the left and right form another, so 4 divided by 2 gives 2 pairs. |
| 3 | 360 degrees. | Four corners at 90 degrees each give 4 times 90, which is 360 degrees. |
| 4 | 4 right angles. | A full turn is 360 degrees, and 360 divided by 90 is 4, so all four angles are right angles. |
| 5 | 115 degrees. | 180 minus 65 gives 115, because adjacent angles on a straight line always add to 180 degrees. |
| 6 | 4 cm both times. | The distance between parallel lines is the same everywhere, so it is 4 cm from any point. |
| 7 | Parallel. | Both a and c are perpendicular to the same line b, so they run in the same direction and a is parallel to c. |
| 8 | 90 degrees. | Neighbouring sides of a rectangle are perpendicular, so they meet at 90 degrees whatever the 12 cm and 5 cm lengths are. |
| 9 | Perpendicular. | AB moves 4 squares sideways and CD moves 4 squares upwards, so a horizontal line meets a vertical line at 90 degrees. |
| 10 | Wrong. Perpendicular only means they meet at 90 degrees; lines of 8 cm and 3 cm can still be perpendicular. | A 8 cm line and a 3 cm line are perpendicular as long as they meet at a right angle; length has nothing to do with it. |
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.
Book a Maths tutorTutor Registration →
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.