# Mathematics Questions and Answers – Special Cases in Polygons

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Special Cases in Polygons”.

1. All the sides of rhombus are _______
a) equal
b) not equal
c) half of the side opposite
d) half of that of adjacent

Explanation: As we know that rhombus is a special type of polygon where all the angles measure acute angle and all the sides of the polygon are equal in length.

2. The diagonals of a rhombus are ______
a) perpendicular to each other
b) perpendicular bisector of each other
c) bisector of each other
d) perpendicular trisector of each other

Explanation: As we know that rhombus is a special type of polygon where all the angles measure acute angle and all the sides of the polygon are equal in length. The diagonals of rhombus have the property that they are perpendicular bisectors of each other i.e. they meet each other at right angle and bisect each other.

3. Rhombus has all the properties of a parallelogram and that of any kite.
a) True
b) False

Explanation: The given statement is true. Rhombus has all the properties of a parallelogram and that of any kite.

4. The diagonals of a rhombus are perpendicular bisectors of one another.
a) True
b) False

Explanation: As we know that rhombus is a special type of polygon where all the angles measure acute angle and all the sides of the polygon are equal in length. The diagonals of rhombus have the property that they are perpendicular bisectors of each other i.e. they meet each other at right angle and bisect each other.

5. What would be the measure of all the angles formed at the center of any rhombus due to its diagonals?
a) 90°
b) 180°
c) 45°
d) Can’t say

Explanation: As we know that rhombus is a special type of polygon, its diagonals are perpendicular bisectors of each other. Hence the measure of all the angles would be 90°.

6. A square is a ______ with equal sides.
a) rectangle
b) kite
c) hexagon
d) trapezium

Explanation: A rectangle has it’s opposite sides equal and all angles are right angles, if all the sides are equal then this figure fulfills all the properties of a square. Hence a square is a rectangle with all sides equal.

7. A square has all properties of which two polygons?
a) Rhombus and Parallelogram
b) Rectangle and Rhombus
c) Parallelogram and Rectangle
d) Circle and Trapezium

Explanation: A square has all the properties of parallelogram and rhombus but not rectangle because it’s all the sides aren’t equal. Hence the correct option would be Rhombus and Parallelogram.

8. The triangle formed by the diagonals of a rectangle and its sides are similar by which test?
a) SAS
b) SSS
c) AA
d) Not similar

Explanation: The triangle formed by a side of a rectangle and the diagonals have,
(i) Side 1 (diagonal)
(ii) Angle (vertically opposite angle)
(iii) Side 2 (diagonal)
Hence the triangles are similar by SAS test of similarity.

9. What is a diagonal?
a) A segment that connects any two nonconsecutive vertices in a polygon.
b) A 90 degree angle.
c) A polygon with four sides.
d) A segment that cuts through a polygon at 45 degrees.

Explanation: A diagonal is a segment which connects alternate sides, here the correct option is ‘A segment that connects any two nonconsecutive vertices in a polygon.’

10. All the squares are rectangles, but all rectangles are not squares.
a) True
b) False

Explanation: Rectangles are four sided closed polygons with opposite sides equal and parallel to each other, but square is a polygon with all sides equal and opposite sides parallel. Therefore the given statement is true and square are considered to be special cases i.e. rectangles with all sides equal.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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