Determining if a Parallelogram ABCD with Measurements 26 and 64 is a Rectangle

Rectangle Identification with Angle Measurement

Is the parallelogram below a rectangle?

AAABBBCCCDDD2664

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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?
00:04 A rectangle is a parallelogram with a right angle
00:07 Let's calculate the angle and check, if it's right then it's a rectangle
00:10 The angle is right therefore the parallelogram is a rectangle
00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is the parallelogram below a rectangle?

AAABBBCCCDDD2664

2

Step-by-step solution

Let's calculate angle B:

64+26=90 64+26=90

The parallelogram in the drawing is indeed a rectangle since a parallelogram with at least one right angle is a rectangle.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Rule: A parallelogram with one right angle is a rectangle
  • Technique: Add given measurements: 64 + 26 = 90 degrees
  • Check: Verify that one angle equals exactly 90 degrees ✓

Common Mistakes

Avoid these frequent errors
  • Assuming measurements are side lengths instead of angles
    Don't treat the numbers 64 and 26 as side lengths = wrong geometric analysis! These represent angle measures that combine to form a right angle. Always identify what the given measurements represent before applying rectangle properties.

Practice Quiz

Test your knowledge with interactive questions

AAABBBDDDCCC90°

The quadrilateral ABCD is a parallelogram.

\( ∢B=90° \)

Is it a rectangle?

FAQ

Everything you need to know about this question

How do I know if the numbers represent angles or sides?

+

Look at the diagram carefully! The numbers 64 and 26 are positioned near an angle, not along the sides. When numbers are at corners or vertices, they usually represent angle measurements.

Why does having one right angle make it a rectangle?

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In a parallelogram, opposite angles are equal and consecutive angles are supplementary. If one angle is 90°, then all four angles must be 90°, making it a rectangle!

What if the angles don't add up to 90 degrees?

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If the angle measurements don't sum to 90°, then it's not a right angle. Without a right angle, the parallelogram cannot be a rectangle - it would just be a regular parallelogram.

Do I need to check all four angles?

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No! In a parallelogram, once you confirm one angle is 90°, the properties guarantee all angles are 90°. That's the beauty of parallelogram angle relationships.

Could this be a rhombus or square instead?

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It could be a square if all sides are equal lengths, but we can't tell from angle measurements alone. However, we can definitively say it's at least a rectangle because of the right angle.

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