You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three non-collinear points in pairs, the figure so obtained is a triangle. Now, let us mark four points and see what we obtain on joining them in pairs in some order.
Let us now recall the angle sum property of a
The sum of the angles of a quadrilateral is 360º. This can be verified by drawing a diagonal and dividing the quadrilateral into two triangles.
Let us perform an activity.
Cut out a parallelogram from a sheet of paper and cut it along a diagonal (see Fig. 8.7). You obtain two triangles. What can you say about these triangles?
Place one triangle over the other. Turn one around, if necessary. What do you observe?
You have studied many properties of a parallelogram in this chapter and you have also
verified that if in a quadrilateral any one of those properties is satisfied, then it becomes
We now study yet another condition which is the least required condition for a quadrilateral to be a parallelogram.
You have studied many properties of a triangle as well as a quadrilateral. Now let us
study yet another result which is related to the mid-point of sides of a triangle. Perform
the following activity.
Draw a triangle and mark the mid-points E and F of two sides of the triangle. Join the points E and F (see Fig. 8.24).
In this chapter, you have studied the following points :
1. Sum of the angles of a quadrilateral is 360°.
2. A diagonal of a parallelogram divides it into two congruent triangles.