Everything Maths Grade 10

Converse

The converse of this theorem states: If a line is drawn through the mid-point of a side of a triangle parallel to
the second side, it will bisect the third side.

VISIT:

You can useGeoGebrato show that the converse of the mid-point theorem is true.

Exercise 7 – 7:

1.PointsCandAare the mid-points on linesBDandBE. Study△EDBcarefully. Identify the third

side of this triangle, using the information as shown, together with what you know about the mid-point

theorem. Name the third side by its endpoints, e.g.,F G.

B

D

E

C

A

2.PointsRandPare the mid-points on linesQSandQT. Study△T SQcarefully. Identify the third side of

this triangle, using the information as shown, together with what you know about the mid-point theorem.

Name the third side by its endpoints, e.g.,F G.

T

S

Q

R

P

3.PointsCandAare given on the linesBDandBE. Study the triangle carefully, then identify and name

the parallel lines.

D

E

C B

A

4.PointsRandPare given on the linesQSandQT. Study the triangle carefully, then identify and name

the parallel lines.

T

Q

S

P

R

264 7.4. The mid-point theorem