Page 124 - NUMINO Challenge_C1

Basic Concepts Bisection of a Parallelogram

Any straight line that passes through the center of a parallelogram divides
the area of the parallelogram in half.

Example Explain why a straight line that passes through the center of a
parallelogram always divides it in half.

AD

E G
F C

B

Class Notes

Since a diagonal line in a parallelogram bisects the other diagonal A D

line, line BE and line DE have the same length. FEB in triangle E G
EBF and GED in triangle EDG are vertical angles, so they are F C
equal. Also, EBF and EDG are alternate interior angles, so they
are equal as well. B

Therefore, triangle and triangle are congruent triangles because one

side and two angles are of the same size.

In the same way as , triangle AFE and triangle CGE; and triangle AED and triangle

CEB are , respectively.

(triangle AFE) (triangle AED) (triangle EDG) AD
(triangle CGE) (triangle CEB) (triangle EBF)
of E G
Therefore, a straight line that passes through the C
F
a parallelogram always bisects it into two equal sections. Remember B
that the area of each section is half the area of the parallelogram.

121Measurement