Question

Which of the following groups is true for $\square ABCD$?

A) ABCD is a Rhombus	a) $\overline {AC} $ and $\overline {BD} $ bisect each other.
B) ABCD is a Parallelogram	b) $\overline {AC} $ and $\overline {BD} $ bisect each other at a right angle.
C) ABCD is a Rectangle	c) $\overline {AC} $ and $\overline {BD} $ are congruent and bisect each other at right angles.
D) ABCD is a Square	d) $\overline {AC} $ and $\overline {BD} $ are congruent and bisect each other.

Options are
(A) $1 - d,2 - a,c - d,4 - c$
(B) $1 - c,2 - d,3 - a,4 - b$
(C) $1 - b,2 - a,3 - d,4 - c$
(D) $1 - b,2 - c,3 - d,4 - a$

Answer 1

Hint: Here two points are given. So, we can find the solution by matching both points. We should know the properties of all shapes.

Complete step-by-step answer:
Now, we compare both part of first point
(A) If ABCD is a rhombus the diagonals of a rhombus intersect at right angles in this case we can say (A) is matched with (b). Which is $\overline {AC} $ and $\overline {BD} $ bisect each other at a right angle
Now we take next point B
(B) If ABCD is a parallelogram we know diagonals of a parallelogram bisect each other So, (B) is match with (a) that is $\overline {AC} $ and $\overline {BD} $ bisect each other.
Now solve another point
(C) That is ABCD is a Rectangle. If diagonals of rectangle are congruent and bisect each other Then according to the given list we can say (C) will match with point (d) that is $\overline {AC} $ and $\overline {BD} $ are congruent and bisect each other.
Here we solve our last point
(D) That is ABCD is a Square then diagonals of square are congruent and bisect each other at right angles then we can say (D) will match with (c).

So, the correct answer is “Option C”.

Note: Here students should see options carefully. They get confused to see so many options, they think there are different points and start solving every option. Students may confuse properties of shape also.