Draw a quadrilateral ABCD and the diagonal AC in what figure does the diagonal divide it.How many such figure sre performed?
Answers
Heyyyy,
he 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 ABCD be a quadrilateral and AC be a diagonal (see Fig. 8.4).
What is the sum of angles in ΔADC?
Fig. 8.4
You know that
∠DAC + ∠ACD + ∠D = 180° (1)
Similarly, in ΔABC,
∠CAB + ∠ACB + ∠B = 180° (2)
Adding (1) and (2), we get
∠DAC + ∠ACD + ∠D + 7ang;CAB + ∠ACB + ∠B = 180° + 180° = 360°
Also, ∠DAC + ∠CAB = ∠A and ∠ACD + ∠ACB = ∠C
So, ∠A + ∠D + ∠B + ∠C = 360°.
i.e., the sum of the angles of a quadrilateral is 360°.
8.3 TYPES OF QUADRILATERALS
Look at the different quadrilaterals drawn below:
Fig. 8.5
Observe that:
One pair of opposite sides of quadrilateral ABCD in Fig. 8.5 (i) namely, AB and CD are parallel. You know that it is called a trapezium.
Both pairs of opposite sides of quadrilaterals given in Fig. 8.5 (ii), (iii) , (iv) and (v) are parallel. Recall that such quadrilaterals are called parallelograms. So, quadrilateral PQRS of Fig. 8.5 (ii) is a parallelogram. Similarly, all quadrilaterals given in Fig. 8.5 (iii), (iv) and (v) are parallelograms.
In parallelogram MNRS of Fig. 8.5 (iii), note that one of its angles namely ∠M is a right angle. What is this special parallelogram called? Try to recall. It is called a rectangle.
The parallelogram DEFG of Fig. 8.5 (iv) has all sides equal and we know that it is called a rhombus.
The parallelogram ABCD of Fig. 8.5 (v) has ∠A = 90° and all sides equal; it is called a square.
6. In quadrilateral ABCD of Fig. 8.5 (vi), AD = CD and AB = CB i.e., two pairs of adjacent sides are equal. It is not a parallelogram. It is called a kite. Note that a square, rectangle and rhombus are all parallelograms.
A square is a rectangle and also a rhombus.
A parallelogram is a trapezium.
A kite is not a parallelogram.
A trapezium is not a parallelogram (as only one pair of opposite sides is parallel in a trapezium and we require both pairs to be parallel in a parallelogram).
A rectangle or a rhombus is not a square.
Answer:
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