Question

Which of these figures must be a rectangle?

Answer 1

Answer:

A rectangle is a parallelogram with at least one right angle is the best choice ⇒ answer A

Step-by-step explanation:

* Lets revise the properties of the rectangle

# Each two opposite sides are parallel

# Each two opposite sides are equal in length

# Its two diagonals bisect each other  and equal each other

# Its four angles are right angles

- The parallelogram can be a rectangle if:

# Two adjacent sides are perpendicular to each other means one

  angle of its four angles is a right angle

- OR

# Its two diagonals are equal in length

* Lets solve the problem

- We will study the answers to chose the best one

# Answer A

- A rectangle is a parallelogram with at least one right angle

∵ Each tow opposite angles are equal in the rectangle

∵ One of the is right angle means its measure is 90°

∴ The measure of the opposite angle is also 90°

∵ The sum of the measures of the four angles is 360°

∴ The sum of the measures of the other two angles is;

   360 - (90 + 90) = 180°

∵ They are equal to each other (opposite angles)

∴ The measure of each one = 180 ÷ 2 = 90°

∴ The measure of the four angles are 90°

∴ The four angles of the rectangle are right angles

* A rectangle is a parallelogram with at least one right angle is the

 best choice