Everything Maths Grade 10

7.3 Quadrilaterals EMA5X

DEFINITION: Quadrilateral

A quadrilateral is a closed shape consisting of four straight line segments.

NOTE:

The interior angles of a quadrilateral add up to 360°.

Parallelogram EMA5Y

DEFINITION: Parallelogram

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Worked example 3: Properties of a parallelogram

QUESTION

ABCDis a parallelogram withAB∥DCandAD∥BC. Show that:

1.AB=DCandAD=BC

2.A^=C^andB^=D^

D C

A B

R

2

3

4

SOLUTION

Step 1: ConnectACto form△ABCand△CDA

Redraw the diagram and draw lineAC.

Step 2: Use properties of parallel lines to indicate all equal angles on the diagram

On your diagram mark all the equal angles.

Step 3: Prove△ABC△CDA

In△ABCand△CDA:

A^ 2 =C^ 3 (alt\s;AB∥DC)

C^ 4 =A^ 1 (alt\s;BC∥AD)

AC (common side)

)△ABC △CDA (AAS)

)AB=CD and BC=DA

)Opposite sides of a parallelogram have equal length.

252 7.3. Quadrilaterals