Parallelogram to Rectangle: Determining Special Properties in Quadrilateral ABCD

Q: What's the difference between a parallelogram and a rectangle?

A parallelogram has opposite sides parallel and equal, but angles can be any size. A rectangle is a special parallelogram where all four angles are exactly 90°.

Q: If I see one angle that's not 90°, is that enough to know it's not a rectangle?

Yes! In a rectangle, all four angles must be 90°. If even one angle is different (like 98° in this problem), it cannot be a rectangle.

Q: How can I tell if an angle is 90° just by looking?

Look for the square corner symbol (⌐) or check if the angle appears to be a perfect 'L' shape. If it looks wider than 90°, it's obtuse. If narrower, it's acute.

Q: Can a parallelogram ever become a rectangle?

Yes! If you adjust a parallelogram so that all its angles become 90°, it transforms into a rectangle. The opposite sides remain parallel and equal.

Q: What if the diagram shows 98° - is that definitely not a right angle?

Correct! 98° is 8° more than a right angle (90°). This makes it an obtuse angle, so the parallelogram cannot be a rectangle.

Rectangle Properties with Angle Recognition

Determine whether the parallelogram below is a rectangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the parallelogram a rectangle?

00:03 A rectangle is a parallelogram with right angles

00:06 It seems that the given angle is not right, therefore not a rectangle

00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine whether the parallelogram below is a rectangle?

Step-by-step solution

The parallelogram in the drawing cannot be a rectangle because in a rectangle all angles are right angles, meaning they are equal to 90 degrees.

Angle A is greater than 90 degrees.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: All four angles must be exactly 90 degrees
Technique: Check if any angle is obtuse (like 98°) or acute
Check: Measure each angle - if any ≠ 90°, not a rectangle ✓

Common Mistakes

Avoid these frequent errors

Thinking parallel sides make a rectangle
Don't assume that parallel opposite sides = rectangle! This only makes it a parallelogram. A parallelogram can have obtuse angles (like the 98° shown), but rectangles need all 90° angles. Always check that every angle equals exactly 90 degrees.

Practice Quiz

Test your knowledge with interactive questions

The quadrilateral ABCD is a parallelogram.

$$ ∢B=90° $$

Is it a rectangle?

FAQ

Everything you need to know about this question

What's the difference between a parallelogram and a rectangle?

A parallelogram has opposite sides parallel and equal, but angles can be any size. A rectangle is a special parallelogram where all four angles are exactly 90°.

If I see one angle that's not 90°, is that enough to know it's not a rectangle?

Yes! In a rectangle, all four angles must be 90°. If even one angle is different (like 98° in this problem), it cannot be a rectangle.

How can I tell if an angle is 90° just by looking?

Look for the square corner symbol (⌐) or check if the angle appears to be a perfect 'L' shape. If it looks wider than 90°, it's obtuse. If narrower, it's acute.

Can a parallelogram ever become a rectangle?

Yes! If you adjust a parallelogram so that all its angles become 90°, it transforms into a rectangle. The opposite sides remain parallel and equal.

What if the diagram shows 98° - is that definitely not a right angle?

Correct! 98° is 8° more than a right angle (90°). This makes it an obtuse angle, so the parallelogram cannot be a rectangle.

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