Construction Class 6 ICSE — Chapter 19 Explained
Construction Class 6 ICSE Maths covers the ruler-and-compass skills you need to copy angles, bisect angles, build standard angles, and draw perpendiculars. This chapter, Construction of Angles, is Chapter 19 in the Class 6 Mathematics book. It walks each construction step by step and finishes with set-squares as a faster tool for the same jobs. The sections below follow the book’s own order, so you can read them alongside the chapter.
Download Construction of Angles Class 6 ICSE Mathematics Chapter 19 PDF
Download the Construction of Angles Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 7 pages, 4 sections, 17 questions.
What is inside Chapter 19
7 pages · 4 sections · 17 exercise questions
| Section | Title |
|---|---|
| 19.1 | RULER AND COMPASS CAN BE USED |
| 19.2 | CONSTRUCTION OF PARTICULAR ANGLES |
| 19.3 | PERPENDICULARS |
| 19.4 | USING SET-SQUARES |
- EXERCISE 19(A): 6 questions
- EXERCISE 19(B): 4 questions
- Revision Exercise (Chapter 19): 7 questions
19.1 RULER AND COMPASS CAN BE USED
The section opens by listing six jobs a ruler and compass can do together. These are the core skills of the whole chapter:
- copy a given angle
- bisect a given angle
- construct certain angles from a given point
- bisect a line segment by drawing its perpendicular bisector
- drop a perpendicular onto a line from an exterior point
- draw a perpendicular at a point on a line
Copying an angle means drawing an equal angle at a new point. Suppose \angle AOB is the given angle and Q is the target point. Follow these steps:
- Draw a line segment QR of any suitable length at Q.
- With O as centre, draw an arc of any suitable radius to cut the arms at C and D.
- With Q as centre, draw an arc of the same radius to cut QR at T.
- Take the distance CD in your compasses. With T as centre, draw an arc of that radius to meet the first arc at S.
- Join QS and extend it to P. Then \angle PQR equals the given \angle AOB.
The first two arcs must share the same radius. The compass carries the distance CD from one drawing to the other. That is why the copied angle matches the original exactly.
Try this with an angle of 40°. The arc from O cuts the arms at C and D, with CD about 2.5 cm. Transfer that 2.5 cm to the new line, and the copied angle matches exactly.
Bisecting splits an angle into two equal halves. With O as centre, draw an arc cutting the arms at C and D. Then:
- With C and D as centres, draw arcs of equal radii to meet at E.
- Join OE. Then \angle AOE = \angle BOE.
The radius of each arc in the first step must be more than half the distance between C and D. If the radius is too small, the arcs will not meet. This is the most common mistake in the chapter.
19.2 CONSTRUCTION OF PARTICULAR ANGLES
The chapter builds angles in a fixed order: 60°, 30°, 90°, 45°, 120°, 135°, 75°. Combinations then give 105°, 15°, 165° and more. Each new angle comes from one you have already drawn.
Start with 60°. Draw a line segment OA. Strike an arc from O to cut OA at B. With B as centre, strike a matching arc to cut the first arc at C. Join OC and extend it to D. Then \angle DOA = 60^\circ.
Bisect that 60° angle and you get two 30° angles. Each half is \angle EOB = 30^\circ.
An angle of 90° has two methods. In the first, step arcs around point O: from B, then from C, then from C and D draw equal arcs to meet at E, and join OE. In the second, cut the line at C and D with two equal arcs from O, then intersect equal arcs from C and D at E. Both give \angle AOE = 90^\circ. In each construction, OE stands perpendicular to OA at point O.
Bisect the 90° angle and each half is 45°.
For 120°, step three equal arcs around point O. For 135°, draw a 90° angle and bisect the other 90° angle beside it.
Work through 75° as a pattern. Draw \angle AOD = 90^\circ at O, then \angle AOE = 60^\circ at the same point. The gap \angle DOE is 30°. Bisect it so \angle EOC = \angle DOC = 15^\circ. Then \angle AOC = 60^\circ + 15^\circ = 75^\circ.
Combinations extend the list: 105^\circ = 90^\circ + 15^\circ, 150^\circ = 90^\circ + 60^\circ, or 150^\circ = 120^\circ + 30^\circ.
19.3 PERPENDICULARS
Construction 10 draws the perpendicular bisector of a segment AB. From A and B, draw arcs of equal radii on both sides of AB. The radius must be more than half the length of AB. The arcs meet at C and D. Join CD; it cuts AB at M. Then AM = BM and \angle AMC = 90^\circ. CD bisects AB and stands perpendicular to it.
Try this with AB = 8 cm. Arcs of radius 5 cm from A and B meet at C and D. Joining CD cuts AB at M, with AM = BM = 4 cm.
Construction 11 drops a perpendicular from a point C outside the line. With C as centre, draw an arc cutting AB at P and Q. From P and Q, draw equal arcs meeting at D on the far side of AB. Join CD; it cuts AB at M. CM is the required perpendicular.
Construction 12 draws a perpendicular through a point M on the line. With M as centre, mark equal arcs cutting AB at P and Q. From P and Q, draw equal arcs meeting at X. Join MX. MX is the perpendicular.
A perpendicular bisector does two jobs at once: it splits the segment into two equal halves and meets it at 90°. A plain perpendicular only meets the line at 90°. These constructions return in the next chapter on triangles, so they are worth mastering now.
19.4 USING SET-SQUARES
A set-square is a triangular piece of plastic or metal. Two types exist in general use:
| Type | Angles it gives |
|---|---|
| 45°-90°-45° set-square | 45^\circ, 90^\circ |
| 60°-90°-30° set-square | 60^\circ, 90^\circ, 30^\circ |
Lines drawn along the sides of a set-square give those angles directly. Placing the two set-squares together gives 75° and 105°.
To draw a perpendicular from an exterior point C, place the set-square so the edge containing 90° lies along AB and the other edge passes through C. Draw along that edge to meet AB at N. CN is the required perpendicular.
To draw a perpendicular at a point C on the line, set the 90° edge along AB at C. Draw CD along the other 90° edge. CD is the required perpendicular.
Set-squares save time, but they do not replace the ruler-and-compass methods. For the full syllabus list, visit the official CISCE board site.
What to practise from Construction Class 6 ICSE
This chapter has three practice blocks. Work through them in the book’s order.
- EXERCISE 19(A) — 6 questions. Copy angles; construct 60°, 90°, 45°, 30°, 120° and 135°; bisect a constructed 60° angle; draw the perpendicular bisector of a given segment and compare the halves; draw a perpendicular at a point on a segment; and draw a perpendicular from an exterior point.
- EXERCISE 19(B) — 4 questions. Use set-squares to build 60° and 90° triangles and measure the joined side; bisect a 120° angle; and build a 75° angle with set-squares plus a joined segment.
- Revision Exercise (Chapter 19) — 7 questions. Mix ruler-and-compass and set-square methods on the same shapes, including measuring results and checking equalities.
EXERCISE 19(A) tests the ruler-and-compass work from sections 19.1 to 19.3. EXERCISE 19(B) tests the set-square methods from section 19.4. The Revision Exercise mixes both sets of tools.
Construction Class 6 ICSE frequently asked questions
How do I construct a 135 degree angle in Construction Class 6 ICSE Maths?
Draw a 90° angle at point O. The line beyond it forms another 90° angle. Bisect that second angle to get two 45° angles. Then \angle AOD = 90^\circ + 45^\circ = 135^\circ.
What is the difference between a perpendicular and a perpendicular bisector in Class 6 ICSE?
A perpendicular meets a line at 90°. A perpendicular bisector also splits the segment into two equal halves. It does both jobs at once.
Which angles can I draw with a set square in Class 6 ICSE?
A 45°-90°-45° set-square gives 45° and 90°. A 60°-90°-30° set-square gives 60°, 90° and 30°. Placing both together gives 75° and 105°.
Why must the arcs in angle bisecting be more than half the distance in this ICSE chapter?
If the radius is less than half the distance between C and D, the two arcs will not reach each other. They need to cross to mark point E.
Reference: ICSE Class 6 Mathematics textbook material, chapter 19: Construction of Angles — CISCE-aligned.