Parallelogram Investigation: Analyzing a Quadrilateral with 95° and 85° Angles

While adjacent angles in a parallelogram do sum to $180°$, this property alone isn't enough! Many other quadrilaterals can have two adjacent angles totaling $180°$. You need all pairs of adjacent angles to sum to $180°$.

You need one of these proofs:

• All angles: Show angles A and B also create the pattern
• Parallel sides: Prove AB || CD and AD || BC
• Equal opposite sides: Show AB = CD and AD = BC
• Opposite angles equal: Show $∠A = ∠C$ and $∠B = ∠D$

Possibly! The given information doesn't rule it out completely. If angles A and B also follow the parallelogram pattern (A + B = $180°$ and opposite angles are equal), then it could be a parallelogram. But we cannot conclude this from the given information alone.

Clear violations include:

• Adjacent angles that don't sum to $180°$
• Opposite angles that aren't equal
• Opposite sides that aren't parallel or equal
• All angles not following the parallelogram pattern

Follow this strategy:

1. List what you know (given angles, sides, etc.)
2. Identify what you need to prove parallelogram
3. Check if you have enough information for any proof method
4. State your conclusion clearly based on sufficient/insufficient evidence