Identifying Angle Types in Parallelogram ABCD: Geometric Analysis

Co-interior Angles with Parallelogram Properties

The parallelogram ABCD is shown below.

What type of angles are indicated in the figure?

AAABBBCCCDDD

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Step-by-step written solution

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1

Understand the problem

The parallelogram ABCD is shown below.

What type of angles are indicated in the figure?

AAABBBCCCDDD

2

Step-by-step solution

To determine the type of angles indicated in a parallelogram, it is crucial to understand the properties of the angles formed by its parallel sides. In any parallelogram, opposite sides are parallel. This means the angles on the same side of the transversal formed by these parallel lines are co-interior angles.

For a parallelogram ABCDABCD, let's focus on the consecutive angles: angle AA and angle DD, or angle BB and angle CC. These consecutive angles are on the same side of the traversal created by the sides. According to the properties of a parallelogram, consecutive angles are supplementary, meaning they add up to 180180^\circ.

In the context of parallel lines and a transversal, such consecutive interior angles are known as "co-interior" angles. They are supplementary and occur when the traversal cuts across the parallel sides of the parallelogram.

Thus, the type of angles indicated in the figure for the parallelogram ABCDABCD are co-interior angles.

Therefore, the correct answer to this problem is Co-interior.

3

Final Answer

Co-interior

Key Points to Remember

Essential concepts to master this topic
  • Property: Co-interior angles on same side of transversal are supplementary
  • Technique: Consecutive angles in parallelogram add up to 180 180^\circ
  • Check: Angle A + Angle D = 180 180^\circ confirms co-interior relationship ✓

Common Mistakes

Avoid these frequent errors
  • Confusing co-interior with alternate angles
    Don't identify angles that are on the same side of the transversal as alternate angles = wrong classification! Alternate angles are on opposite sides of the transversal and equal, while co-interior angles are on the same side and supplementary. Always check which side of the transversal the angles are located.

Practice Quiz

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If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

How can I remember the difference between co-interior and alternate angles?

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Co-interior means "together inside" - they're on the same side of the transversal and add up to 180 180^\circ . Alternate means they alternate sides and are equal!

Why are co-interior angles always supplementary in a parallelogram?

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Because opposite sides of a parallelogram are parallel! When a transversal cuts parallel lines, co-interior angles must add to 180 180^\circ - it's a fundamental property.

Are all consecutive angles in a parallelogram co-interior?

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Yes! Any two consecutive angles in a parallelogram are co-interior because they're on the same side of the transversal formed by the parallel sides.

What if the figure wasn't a parallelogram - would the angles still be co-interior?

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The angles could still be co-interior by position, but they wouldn't necessarily be supplementary. The 180 180^\circ rule only works when the lines are parallel!

How do I identify the transversal in this problem?

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Look for the line that cuts across the parallel sides. In parallelogram ABCD, sides AD and BC act as transversals cutting the parallel sides AB and DC.

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