2 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) $ \angle a = \angle c $ (ans.) (2) given the intersection point of ac and bd is o, $ ao = co $ (ans.) (3) $ ab = cd $ (ans.), (4) $ ad \parallel 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.)

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Accepted Answer

### Question 2 Solutions:
#### (1)
# Explanation:
## Step1: Recall parallelogram angle condition
In a parallelogram, both pairs of opposite angles are equal. So if $ \angle A=\angle C $, the missing part is $ \angle B = \angle D $.
# Answer: $ \angle B=\angle D $

#### (2)
# Explanation:
## Step1: Recall parallelogram diagonal condition
In a parallelogram, the diagonals bisect each other. So if $ AO = CO $ (O is the intersection of diagonals AC and BD), then $ BO=DO $.
# Answer: $ BO = DO $

#### (3)
# Explanation:
## Step1: Recall parallelogram side condition
In a parallelogram, both pairs of opposite sides are equal. So if $ AB = CD $, the other pair of opposite sides must be equal, i.e., $ AD=BC $. Also, another valid condition with $ AB = CD $ is that $ AB\parallel CD $ (since equal and parallel sides imply parallelogram, but for the "missing part" with $ AB = CD $, the main opposite side equality is $ AD = BC $, and also $ AB\parallel CD $ can be considered, but the standard pair for $ AB = CD $ is $ AD=BC $ and $ AB\parallel CD $ (but the two answers here are $ AD = BC $ and $ AB\parallel CD $). Wait, the problem says "Question (3), and (4) will have two answers". For $ AB = CD $, the two missing parts (to make it a parallelogram) are $ AD = BC $ (opposite sides equal) and $ AB\parallel CD $ (opposite sides parallel, and equal + parallel implies parallelogram). But more accurately, the two conditions with $ AB = CD $ to form a parallelogram are $ AD = BC $ (opposite sides equal) and $ AB\parallel CD $ (opposite sides parallel, and if a pair of opposite sides are equal and parallel, it's a parallelogram). So the two answers are $ AD = BC $ and $ AB\parallel CD $.
# Answer: $ AD = BC $, $ AB\parallel CD $

#### (4)
# Explanation:
## Step1: Recall parallelogram side parallel condition
In a parallelogram, both pairs of opposite sides are parallel. So if $ AD\parallel BC $, the other pair of opposite sides must be parallel, i.e., $ AB\parallel CD $. Also, another valid condition with $ AD\parallel BC $ is that $ AD = BC $ (since parallel and equal sides imply parallelogram). So the two answers are $ AB\parallel CD $ and $ AD = BC $.
# Answer: $ AB\parallel CD $, $ AD = BC $

### Question 3 Solutions:
#### (1)
# Explanation:
## Step1: Recall parallelogram with equal diagonals
A rectangle is a parallelogram (since it has opposite sides equal and parallel, opposite angles equal) and its diagonals are equal in length. Also, a square is a special case of a rectangle, but the main one is rectangle (and square, but rectangle is the general case).
# Answer: Rectangle (Square is also correct, but Rectangle is the primary answer)

#### (2)
# Explanation:
## Step1: Recall parallelogram with adjacent sides equal
A rhombus is a parallelogram where all sides are equal, so adjacent sides are equal. A square is also a rhombus (and a parallelogram) with adjacent sides equal. But the main one is rhombus.
# Answer: Rhombus (Square is also correct, but Rhombus is the primary answer)

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QUESTION IMAGE

Question

Explanation:

Question 2 Solutions:

(1)

Step1: Recall parallelogram angle condition

Step1: Recall parallelogram diagonal condition

Step1: Recall parallelogram side condition

Answer:

(2)