How do I prove that if a quadrilateral has consecutive angles that are supplementary, then it is a parallelogram?

Answer 1

Not necessary

Consider a trapezoid with angles 35-135-90-90. It has 2 instances of consecutive (adjacent?) angles that are supplementary (35-135 and 90-90) but it is not a parallelogram

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To prove that if a quadrilateral has consecutive angles that are supplementary, then it is a parallelogram, you can use the following approach:

  1. Start by labeling the quadrilateral vertices as ( A), ( B), ( C), and ( D), in clockwise or counterclockwise order.
  2. Assume that consecutive angles are supplementary. That is, angle ( A) + angle ( B) = 180 degrees, angle ( B) + angle ( C) = 180 degrees, angle ( C) + angle ( D) = 180 degrees, and angle ( D) + angle ( A) = 180 degrees.
  3. Consider the properties of supplementary angles to prove that opposite angles are equal. Since angle ( A) + angle ( B) = 180 degrees, and angle ( C) + angle ( D) = 180 degrees, then angle ( A) = angle ( C) and angle ( B) = angle ( D).
  4. Use the fact that opposite angles are equal to show that opposite sides are parallel. This follows from the properties of angles formed when a transversal intersects parallel lines.
  5. Therefore, if opposite sides of a quadrilateral are parallel, it is a parallelogram.

By demonstrating these steps, you establish that a quadrilateral with consecutive supplementary angles must be a parallelogram.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7