Question 5 of 11beginner🔧 ApplyShort Answer3 marks

Construct at least 4 different angles. Draw their bisectors.

Correct Answer

Step 1: Draw an angle ∠XOY.

Step 2: With O as centre and any convenient radius, draw an arc cutting OX at A and OY at B.

Step 3: With A as centre and any radius greater than half of AB, draw an arc.

Step 4: With B as centre and the same radius, draw another arc intersecting the previous arc at C.

Step 5: Join OC. OC is the angle bisector of ∠XOY.

Why it works: Triangles OAC and OBC are congruent by SSS (OA = OB, AC = BC, OC is common), making ∠AOC = ∠BOC.

Exercise: Figure it Out (Section 3) | Q: 1 | (Page Page 9)
For More Understanding

Explanation

The chapter explains angle bisection using congruent triangles. When OA = OB (by construction) and AC = BC (by using the same radius), triangles OAC and OBC are congruent by the SSS condition. Therefore, ∠AOC = ∠BOC, meaning OC bisects the angle. Students should practice this construction with various angles (acute, obtuse, right angles) to develop proficiency.

Solution Steps

  1. Draw an angle ∠XOY.

  2. With O as centre and any convenient radius, draw an arc cutting OX at A and OY at B.

  3. With A as centre and any radius greater than half of AB, draw an arc.

  4. With B as centre and the same radius, draw another arc intersecting the previous arc at C.

  5. Join OC. OC is the angle bisector of ∠XOY.

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