NCERT Solutions for Class 7th Maths Chapter 6 Steps for Angle Bisection — In-text Questions
Book page 144 Updated on2026-09-19
Q1.
How do we construct these congruent triangles, given the angle?
Answer
Make the three pairs of sides equal, and SSS does the rest.
On the two arms of ∠XOY mark A and B with OA = OB (one compass opening from O)
From A and from B cut arcs of one equal radius, meeting at C ⇒ AC = BC
OC is common to both triangles
In ΔOAC and ΔOBC:
OA = OB, AC = BC, OC = OC
⇒ ΔOAC ≅ ΔOBC by SSS
⇒ ∠AOC = ∠BOC ⇒ OC bisects ∠AOB
OA = OB from one arc; AC = BC from two equal arcs. SSS makes ΔOAC ≅ ΔOBC, so OC bisects the angle.
Why it happens: the compass can only do two things — carry a length and draw equal distances. Both congruent sides we need are of that kind: OA = OB is one sweep from O, and AC = BC is one radius used twice. SSS then forces the two angles at O to be equal, without any measuring.
Tip: the radius used for the arcs from A and B need not equal OA. It only has to be big enough for the two arcs to cross.