Parallelogram Side Length: Finding X When Adjacent Side is 15

Q: How do I know which sides are opposite in a parallelogram?

Opposite sides are the ones that don't share a vertex. In parallelogram ABCD, side AB is opposite to side DC, and side AD is opposite to side BC. They're parallel and never touch!

Q: Why can't I set adjacent sides equal?

Adjacent sides share a vertex and can have different lengths! Only opposite sides must be equal in a parallelogram. Setting adjacent sides equal would make it a rhombus, which is a special type of parallelogram.

Q: What if the diagram looks like a rectangle?

Even if it looks rectangular, treat it as a general parallelogram unless told otherwise. The key property remains: opposite sides are equal, regardless of the angles.

Q: How can I double-check my answer?

Substitute your values back: if $ x = 15 $ and $ y = 7 $, then AB = DC = 15 and AD = BC = 7. Both pairs of opposite sides are equal! ✓

Parallelogram Properties with Opposite Side Equality

Look at the quadrilateral in the diagram below.

What is the value of x if the quadrilateral ABCD is a parallelogram?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the quadrilateral in the diagram below.

What is the value of x if the quadrilateral ABCD is a parallelogram?

Step-by-step solution

To find the values of $x$ and $y$ for the parallelogram ABCD, we use the property that opposite sides of a parallelogram are equal.

1. Opposite sides AB and DC must be equal, therefore:

x = 15

2. Opposite sides AD and BC must also be equal, therefore:

y = 7

Thus, the values of the unknowns that make ABCD a parallelogram are $x = 15$ and $y = 7$ .

This corresponds to choice 1: $x = 15, y = 7$ .

Final Answer

x=15 , y=7

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of a parallelogram are always equal in length
Technique: Side AB equals side DC, so x = 15
Check: Verify both pairs: AB = DC and AD = BC ✓

Common Mistakes

Avoid these frequent errors

Confusing adjacent sides with opposite sides
Don't set adjacent sides equal like AB = BC! Adjacent sides can be different lengths, leading to wrong equations. Always identify opposite sides: AB = DC and AD = BC.

Practice Quiz

Test your knowledge with interactive questions

It is possible to draw a quadrilateral that is not a rectangle and that has two equal opposite sides?

FAQ

Everything you need to know about this question

How do I know which sides are opposite in a parallelogram?

Opposite sides are the ones that don't share a vertex. In parallelogram ABCD, side AB is opposite to side DC, and side AD is opposite to side BC. They're parallel and never touch!

Why can't I set adjacent sides equal?

Adjacent sides share a vertex and can have different lengths! Only opposite sides must be equal in a parallelogram. Setting adjacent sides equal would make it a rhombus, which is a special type of parallelogram.

What if the diagram looks like a rectangle?

Even if it looks rectangular, treat it as a general parallelogram unless told otherwise. The key property remains: opposite sides are equal, regardless of the angles.

How can I double-check my answer?

Substitute your values back: if $x = 15$ and $y = 7$ , then AB = DC = 15 and AD = BC = 7. Both pairs of opposite sides are equal! ✓

What if there are more variables in the problem?

The same rule applies! Set up one equation for each pair of opposite sides. You'll get a system of equations that you can solve step by step.

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