**Definition of Bisect**

- Bisect means to divide into two equal sections or two equal halves.

**More about Bisect**

- If we bisect a 90° angle, we will have two 45° angles.

- The word ‘bisect’ combines the common Latin ‘bi’ for ‘two’, and ‘secare’, meaning ‘to cut’, which also is the root for secant.
- Straight edge and compass are used to bisect a line segment or an angle.
- Anything can be bisected: a line, an angle, a circle, a square.

**Example of Bisect**

- Following steps are involved when we bisect an angle by using ruler and compass:

Draw an arc with B as the centre to cut the arms, BA and BC, of the angle at P and Q respectively.

Using the same radius, draw an arc centered at P.

Again, using the same radius, draw an arc centered at Q to cut the arc previously drawn at R.

Join, B, the vertex of the angle, to the point R.

BRbisects the angleABC, and is called the bisector of the angleABC.

**Solved Example on Bisect**

Find the value of DC, if bisects ΔBAC.

Choices:

A. 2 cm

B. 8 cm

C. 4 cm

D. 6 cm

Correct Answer: C

Solution:

Step 1:≅

Step 2:m∠BAD =m∠DAC

Step 3:≅ [Same side.]

Step 4:ΔBAD ≅ ΔCAD [SAS Postulate.]

Step 5:≅ [Step4.]

Step 6:DC = 4 cm [D is the midpoint of BC.]

**Related Terms for Bisect**

- Halves
- Two halves
- Line segment