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

The parallelogram ABCD is shown below.

What type of angles are indicated in the figure?

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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