Everything Maths Grade 10

6.Find the area ofACDFifAB= 8; BF= 17; F E=EC; BE=ED;A^= 90◦; CED^ = 90◦.



6

C

.

1

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1.2G78 2.2G79 3.2G7B 4.2G7C 5.2G7D 6.2G7F

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7.4 The mid-point theorem EMA66

Investigation: Proving the mid-point theorem

B C

A

D E

1.Draw a large scalene triangle on a sheet of paper.

2.Name the verticesA,BandC. Find the mid-points (DandE) of two sides and connect them.

3.Cut out△ABCand cut along lineDE.

4.Place△ADEon quadrilateralBDECwith vertexEon vertexC. Write down your observations.

5.Shift△ADEto place vertexDon vertexB. Write down your observations.

6.What do you notice about the lengthsDEandBC?

7.Make a conjecture regarding the line joining the mid-point of two sides of a triangle.

Worked example 8: Mid-point theorem

QUESTION

Prove that the line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half

the length of the third side.

262 7.4. The mid-point theorem