Unit 1: Quadrilaterals and midpoint theorem
What is a quadrilateral?
- A polygon is a two-dimensional figure with three or more straight sides.
- A quadrilateral is a polygon with four straight sides.
Types of quadrilaterals
Watch the interactive video below on Quadrilaterals and Triangles and answer the questions that appear.
Click on the infographic below to see the sufficient conditions to prove quadrilaterals.
Example
- PORS is a parallelogram
- PT = TS, OU = UR
Prove that TURS is a parallelogram.
How to answer the question
- Analyse the diagram. Remember the use of properties of a parallelogram as discussed above. Using colour is helpful
- Given: PORS is a parallelogram
- Properties of a parallelogram
- Two pairs of opposite sides are parallel and equal
- PS = OR and PO = SR
- PS || OR and PO || SR
Prove
Midpoint theorem
- The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half the third side. (Special case to proportionality)
In ΔΔABC, M and N are the midpoints between AB and AC respectively.
Prove the theorem that states:
- MN || BC
- MN = 1212BC