Understanding Quadrilaterals MCQs

Ans. Triangle (Option C)

Explanation: Triangle is a three-sided polygon whereas a Quadrilateral stands for a four-sided polygon. Quadrilaterals include shapes that have four sides such as a Rectangle, Square, Trapezoid, Kite, or uneven and characterized. Quadrilaterals are usually two-dimensional figures that have four sides in total and have four vertices and corners. 

Ans. Square (Option B)

Explanation: Square is considered to be a regular Quadrilateral because it includes four equal sides as well as angles. Also, a square has both its sides and angles equal to each other. Similar to that of a rectangle, a square has four angles of 90° each. Apart from all these properties, a square can also be seen as a rectangle that has two adjacent sides as equals.

Ans. 110° (Option A)

Explanation: ∠A + ∠B = 180°

70° + ∠B = 180°

∠B = 180° - 70° = 110°

The adjacent angles of a parallelogram are supplementary. As a result, the sum of any two adjacent parallelogram angles equals 180°. As a result, it is demonstrated that any two adjacent or successive parallelogram angles are supplementary.

Ans. Rhombus (Option A)

Explanation: A square is a four-sided figure with diagonals that intersect at right angles. A rhombus is a square's appropriate subset. When every angle is a right angle, it forms a square. As a result, the diagonals of a rhombus intersect at right angles. 

Ans. Only statement 2 is true. (Option A)

Explanation: A rectangle's diagonals are equal in length but do not intersect each other perpendicularly. As a result, the third statement is untrue. Since not all parallelogram diagonals intersect each other perpendicularly, the fourth statement is similarly incorrect.

Rhombus diagonals bisect each other perpendicularly. Hence, the correct answer is the first statement.

Ans. A Quadrilateral can have the utmost three angles (Option C)

Explanation: As per the properties of Quadrilaterals, every Quadrilateral has four vertices, four angles, four sides and the total of all its interior angles forms 360°. Also, each diagonal of a quadrilateral divides it into two separate triangles which also proves that quadrilaterals have two diagonals. Hence, the third option that states Quadrilateral can have utmost three angles is proven to be incorrect.

Ans. All of the above (Option D)

Explanation: According to geometry, a quadrilateral is a covered, two-dimensional object with four straight sides. Four vertices, also known as corners, make up the polygon. Rectangles, squares, trapezoids, kites, and uneven and uncharacterized shapes are all examples of quadrilaterals. Assuming that ABCD is a quadrilateral that has four angles that are interior, four sides and four vertices. Hence, Option D is the correct answer. 

Ans. 144° (Option D)

Explanation: Considering ABCD as a quadrilateral.

Let angle A be X

Therefore, 

X + 2x + 3x+ 4x = 360° (Sum of all angles of a Quadrilateral)

X = 36°

Hence, the greatest angle in terms of measurements is 4x = 4 ? 36 = 144°

Ans. Collinear (Option C)

Explanation: As has been stated that the area of quadrilateral ABCD is zero. In a quadrilateral, any three points have the ability to form a triangle, hence, four such triangles can be formed. Considering the area of ABCD as zero, it also means that the area of the triangle formed by the three points is also zero which further means that they are collinear as per the Area of Triangle method. The area of triangle method mentions that three points are proved to be collinear if the triangle is formed by the three points zero. Therefore, it can be concluded that any triangle formed within a quadrilateral will have its area zero. Hence, points A, B, C and D are collinear. 

Ans. No (Option D)

Explanation: As per the Angle Sum Property, the sum of angles of a quadrilateral is 360°.

Given angles: 80°, 110°, 70° and 95°

Therefore, 80°+ 110°+ 70° + 95°

190° + 165° = 355°

Since the sum of the given angles, 355° is not equal to 360°, therefore, all the four given angles are not that of a Quadrilateral. Hence, the correct answer is Option D.

Ans. Parallelogram (Option D)

Explanation: A parallelogram's diagonal splits it into two congruent triangles, and we know that congruent figures have the same area. As a result, a parallelogram will be formed by such a quadrilateral. As a result, the solution is a parallelogram.