Problem Set 27 – Parallel and Perpendicular LinesClass 5 Maths · Chapter 6 Angles · Problem Set 27 – Maharashtra Board

Summary: Problem Set 27 – Parallel and Perpendicular Lines

A right angle measures 90°. An acute angle is less than 90°. An obtuse angle is more than 90°.

You can make a right angle by folding a paper twice: fold it once, then fold the folded edge onto itself.

Parallel lines never meet or cut each other, however far they go. They can be of different lengths.

Perpendicular lines meet at a right angle (90°). A small square at the corner shows this.

Examples: rails of a railway track are parallel; a door frame's side and the floor are perpendicular.

Key points to remember

• Right angle = 90°
• Acute angle < 90°; obtuse angle > 90°
• Fold paper twice to make a right angle
• Parallel lines never meet
• Parallel lines can have different lengths
• Perpendicular lines make a 90° angle
• A small square mark shows a right angle
• Both edges of a ruler make parallel lines

Problem Set 27 – Parallel and Perpendicular Lines – Notes

1. Three types of angles

• Right angle: exactly 90°, like the corner of a slate.
• Acute angle: less than 90°, like the tip of a pizza slice.
• Obtuse angle: more than 90°, like a laptop screen pushed far back.

2. Fold a right angle

• Take any scrap of paper and fold it roughly in half. Press the fold.
• Now fold again so that the first fold lies exactly on top of itself.
• Open the paper. The two fold lines cross at right angles. Check with a protractor: 90°.

3. Parallel lines

• Parallel lines run side by side and keep the same gap between them. They never cross.
• Examples: the two rails of a railway track, the lines on a notebook page, the steps of a ladder.
• Draw them: hold a ruler still and draw along both of its long edges. You get two parallel lines.
• One line may be shorter than the other — they are still parallel if they never meet when extended.

4. Perpendicular lines

• Two lines that meet at 90° are perpendicular to each other.
• Examples: a flagpole and the ground; two touching edges of a book; the margin line and a printed line on a notebook page.
• We draw a small square in the corner to show that the lines are perpendicular.

5. Telling them apart

• Ask: do the lines ever meet? If never → parallel.
• If they meet, measure the angle. If it is 90° → perpendicular.
• If they meet at some other angle (like 50°), they are neither parallel nor perpendicular.

Formulas at a glance

Key terms

Problem Set 27 – Parallel and Perpendicular Lines – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 27 – Parallel and Perpendicular Lines – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 27 – Parallel and Perpendicular Lines

⏱ About 20 minutes

1. Learn (5 min)
   Learn the meaning of parallel and perpendicular, and the three angle types.
2. Look around (10 min)
   Find 3 pairs of parallel lines and 3 pairs of perpendicular lines at home. Fold paper to make a right angle.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.