# 9th Class Math Chapter 12 Line Bisectors and Angle Bisectors Short Questions Answer

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## 9th Class Math Chapter 12 Line Bisectors and Angle Bisectors Short Questions Answer

Define the following.

Bisector of a line segment:
A line passing through the midpoint of a segment is called the bisector of line segment.
Bisector of an angle:
A ray that bisects an angle is called bisector of the angle.

The given triangle ABC is equilateral triangle and AD is bisector of angle Az then fond the values of unknown x°, y° and z°.

Solution: ∆ABC is equilateral
mA = mB = mC = 60°
° = 60°
x° = y° = mA
= ½ (60°) = 30°
x° = y° = 30° In the given congruent triangles LMO and LNO, find the unknowns x and m.

Solution:
Corresponding sides of congruent triangles ∆LMO and ∆LNO.
LM ≅ LN
∴ 2x + 6 = 18
⟹ 2x = 18 – 6 = 12
x = 12/2 = 6
Given that mON = 12
Since given triangles are congruent therefore mOM = mON = 12
mOM = m = 12

CD is the right bisector of the line segment AB
If m AB = 6 cm, then find the m AL and m LB
If m BD = 4 cm, then find the m AD

Solution:
CD is right bisector
∴ AL ≅ BL
∴ mAL = mBL
= ½ m AB = ½ (6cm) = 3cm m AL = m BL = 3cm
In ∆ALD ↔ ∆BLD
AL ≅ BL
BLD ≅BLD
and DL ≅ DL
∆ALD ≅ ∆BLD
So, m AD ≅ m BQ = 4cm