Diagonals of a Quadrilateral

Q.

I draw a quadrilateral and then draw all its diagonals.How many triangles can I find?

1. 3

2. 2

3. 8

4. 1

Q.

If the diagonals of a quadrilateral bisect each other at ${90}^{\circ }$, then the quadrilateral is a

1. Square

2. Rectangle

3. Rhombus

4. Parallelogram

Q. Name the adjacent angles of the given quadrilateral

1. $(\angle D$, $\angle C)$ , $(\angle C$, $\angle B)$, $(\angle B$, $\angle A)$, $(\angle A$, $\angle D)$
2. $(\angle D$, $\angle C)$ , $(\angle A$, $\angle C)$, $(\angle B$, $\angle D)$, $(\angle A$, $\angle D)$
3. $(\angle D$, $\angle A)$ , $(\angle A$, $\angle C)$, $(\angle B$, $\angle A)$, $(\angle D$, $\angle B)$
4. $(\angle D$, $\angle B)$ , $(\angle C$, $\angle A)$, $(\angle B$, $\angle A)$, $(\angle A$, $\angle D)$

Q.

Statement 1: Sum of the interior angles of a quadrilateral is ${360}^{\circ }$.

Statement 2: A diagonal divides the quadrilateral into two triangles. The sum of angles of a triangle is ${180}^{\circ }$.

1. Statement 1 is correct and statement 2 wrong

2. Both statements are correct and statement 2 has sufficient information to prove statement 1

3. Both statements are correct but statement 2 doesn’t have sufficient information to prove statement 1

4. Both statements are wrong.

Q. In the following figure, AC and BD are the diagonals of quadrilateral ABCD. If AC is perpendicular to BD , then which of the following angles is not the right angle?

1. $\angle APD$
2. $\angle CPD$
3. $\angle BPC$
4. $\angle PBC$

Q.

Question 2(d):

Draw a rough sketch of a quadrilateral KLMN.

State: Two pairs of adjacent angles.

Q. Identify the pairs of adjacent sides, Opposite sides and Diagonals in the quadrilateral ABCD. [3 Marks]

Q. In the following figure, AC and BD are the diagonals of quadrilateral ABCD. If AC is perpendicular to BD , then which of the following angles is not the right angle?

1. $\angle APD$
2. $\angle CPD$
3. $\angle BPC$
4. $\angle PBC$