Quadrilateral ABCD with Parallel Sides: Rectangle Classification Problem

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

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

Q: Can a quadrilateral with parallel sides still not be a rectangle?

Absolutely! Parallelograms, rhombuses, and trapezoids can all have parallel sides without being rectangles. The key is that rectangles need all angles to be 90°.

Q: How can I quickly identify if a shape is a rectangle?

Check if opposite sides are parallelVerify that all four angles equal 90°If both conditions are met, it's a rectangle!

Q: What if the diagram looks like a rectangle but has different angle measures?

Always trust the given measurements over visual appearance! Diagrams aren't always drawn to scale, so rely on the numerical angle values provided.

Rectangle Properties with Angle Constraints

Given the quadrilateral ABCD whereby

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

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Understand the problem

Given the quadrilateral ABCD whereby

AD||BC , AB||CD

Indicate if the quadrilateral is a rectangle.

Step-by-step solution

In a rectangle, it is known that all angles measure 90 degrees.

Since we know that angle B is equal to 100 degrees, the quadrilateral cannot be a rectangle.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: All four angles must measure exactly 90 degrees
Technique: Check each angle measurement, like the 100° angle shown
Check: If any angle ≠ 90°, then not a rectangle ✓

Common Mistakes

Avoid these frequent errors

Assuming parallel sides make a rectangle
Don't think parallel sides automatically mean rectangle = wrong classification! Parallelograms also have parallel opposite sides but aren't rectangles. Always check that all angles equal 90° to confirm rectangle properties.

Practice Quiz

Test your knowledge with interactive questions

It is possible to draw a quadrilateral that is not a rectangle, with the sum of its two adjacent angles equaling 180?

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, but angles can be any measure. A rectangle is a special parallelogram where all angles are exactly 90°.

Can a quadrilateral with parallel sides still not be a rectangle?

Absolutely! Parallelograms, rhombuses, and trapezoids can all have parallel sides without being rectangles. The key is that rectangles need all angles to be 90°.

Why does one non-90° angle disqualify the whole shape?

In any quadrilateral, the angles must add up to 360°. If one angle is not 90°, then at least one other angle cannot be 90° either, breaking the rectangle rule.

How can I quickly identify if a shape is a rectangle?

Check if opposite sides are parallel
Verify that all four angles equal 90°
If both conditions are met, it's a rectangle!

What if the diagram looks like a rectangle but has different angle measures?

Always trust the given measurements over visual appearance! Diagrams aren't always drawn to scale, so rely on the numerical angle values provided.

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