Question 1

A diagonal of a parallelogram divides it into two triangles which are:

Accepted Answer

A diagonal of a parallelogram divides it into two congruent triangles. This can be proven using the SAS (Side-Angle-Side) congruence criterion, as the alternate interior angles are equal and the diagonal is common to both triangles.

Question 2

If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then the measure of the largest angle is:

Accepted Answer

Let the angles be 3x, 5x, 9x, and 13x. The sum of angles in a quadrilateral is 360 degrees. Therefore, 3x + 5x + 9x + 13x = 360, which gives 30x = 360, so x = 12. The largest angle is 13x = 13 12 = 156 degrees.

Question 3

Which of the following is not true for a parallelogram?

Accepted Answer

The diagonals of a parallelogram bisect each other, opposite sides are equal, and opposite angles are equal. However, the diagonals are not necessarily equal in length; they are equal only in rectangles and squares.

Question 4

If the diagonals of a quadrilateral bisect each other at right angles, then the quadrilateral is a:

Accepted Answer

When the diagonals of a quadrilateral bisect each other at 90 degrees, the quadrilateral is a rhombus. A kite has diagonals intersecting at right angles, but they do not necessarily bisect each other completely.

Question 5

The line segment joining the mid-points of any two sides of a triangle is:

Accepted Answer

According to the Mid-point Theorem, the line segment joining the mid-points of two sides of a triangle is parallel to the third side and is half of it.

Quadrilaterals