bisect


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.

BR bisects the angle ABC, and is called the bisector of the angle ABC.

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