Question

the following statements (1) to (4) represent the conditions for quadrilateral abcd to be called a parallelogram. add the missing part of each condition. question (3), and (4) will have two answers.
(1) ∠a = ∠c
(ans) ∠b = ∠d
(2) given the intersection point of ac and bd is o,
ao = co
(ans) bo = do
(3) ab = cd
(ans)
(4) ad || bc
(ans)
3 name the quadrilateral that fits to the following descriptions.
(1) a parallelogram where the diagonals are equal in length.
(ans)
(2) a parallelogram where the adjacent sides are equal.
(ans)

Explanation:

Question 2 (3)

Step1: Recall parallelogram side condition

A quadrilateral is a parallelogram if both pairs of opposite sides are equal.

Step2: Apply to given side

Given \( AB = CD \), the missing part is \( AD = BC \) to satisfy both pairs of opposite sides equal.

Question 2 (4)

Step1: Recall parallelogram side/angle conditions

A quadrilateral is a parallelogram if: (1) both pairs of opposite sides are parallel, or (2) one pair of opposite sides is parallel and supplementary consecutive angles, or (3) one pair of opposite sides is parallel and equal. Given \( AD \parallel BC \), the missing part can be \( AB \parallel CD \) (to have both pairs of opposite sides parallel) or \( \angle A + \angle B = 180^\circ \) (supplementary consecutive angles imply parallel sides).

Step2: Choose a common condition

We choose \( AB \parallel CD \) as a direct opposite - side parallel condition.

Question 3 (1)

Step1: Recall parallelogram with equal diagonals

Among parallelograms, a rectangle is defined as a parallelogram where the diagonals are equal in length. This is a key property that distinguishes a rectangle from other parallelograms (like rhombus or general parallelogram).

Step2: Confirm the property

In a parallelogram, if diagonals are equal, it must be a rectangle (this can be proven using triangle congruence in the parallelogram, but for the purpose of this question, we use the known property).

Question 3 (2)

Answer:

\( AD = BC \)