Parallelogram Proof: Can Equal 115° Angles Determine a Quadrilateral's Type?

Parallelogram Properties with Insufficient Angle Information

Given the quadrilateral ABCD where:

A=115° ∢A=115°

y D=115° ∢D=115°

AAABBBDDDCCC115°115°

Is it possible to conclude that this quadrilateral is a parallelogram?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the quadrilateral ABCD where:

A=115° ∢A=115°

y D=115° ∢D=115°

AAABBBDDDCCC115°115°

Is it possible to conclude that this quadrilateral is a parallelogram?

2

Step-by-step solution

Given that a parallelogram is a quadrilateral whose two pairs of sides are parallel, and in the figure only two angles are given to us.

We do not have enough data to determine and prove whether angles C and B are equal to each other.

Therefore, the quadrilateral is not a parallelogram.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Parallelogram Rule: Opposite angles must be equal and consecutive angles supplementary
  • Technique: Check if A+B=180° ∢A + ∢B = 180° and A=C ∢A = ∢C
  • Check: Verify all four angle relationships before concluding parallelogram ✓

Common Mistakes

Avoid these frequent errors
  • Assuming two equal angles prove parallelogram
    Don't conclude parallelogram from just A=D=115° ∢A = ∢D = 115° = wrong conclusion! Two equal angles could exist in any quadrilateral without making it a parallelogram. Always verify that opposite angles are equal AND consecutive angles are supplementary.

Practice Quiz

Test your knowledge with interactive questions

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 13.

BD = 6 and AC = 4

AAABBBDDDCCC134615

Is it possible to conclude that this quadrilateral is a parallelogram?

FAQ

Everything you need to know about this question

What makes a quadrilateral a parallelogram?

+

A parallelogram needs both pairs of opposite sides parallel, which means opposite angles must be equal and consecutive angles must be supplementary (add to 180°).

Why isn't knowing two angles enough?

+

You need information about all four angles! Even if A=D=115° ∢A = ∢D = 115° , angles B and C could be anything as long as the sum equals 360°. This isn't enough to guarantee parallelogram properties.

What would I need to prove it's a parallelogram?

+

You'd need to show that opposite angles are equal: A=C ∢A = ∢C and B=D ∢B = ∢D , OR that consecutive angles are supplementary: A+B=180° ∢A + ∢B = 180° .

Could this quadrilateral be something else?

+

Yes! It could be a trapezoid, kite, or irregular quadrilateral. Having A=D=115° ∢A = ∢D = 115° doesn't eliminate other possibilities since we don't know angles B and C.

How do I check my reasoning?

+

Always ask: "Do I have enough information to prove ALL the required properties?" For parallelograms, you need evidence about both pairs of opposite angles or sides, not just one pair.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram for Ninth Grade questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations