Rectangle Congruence: Comparing 4×8 and 8×4 Rectangles

Q: How can rectangles with different orientations be congruent?

Congruent figures have the same size and shape, even if rotated! A 4×8 rectangle turned 90° becomes an 8×4 rectangle - they're still exactly the same rectangle.

Q: What's the difference between congruent and similar rectangles?

Congruent rectangles are exactly the same size and shape. Similar rectangles have the same shape but can be different sizes. These 4×8 and 8×4 rectangles are congruent!

Q: Would a 2×16 rectangle be congruent to these?

No! Even though $ 2 \times 16 = 32 $ (same area), the sides are different lengths. For congruence, you need matching pairs of sides: both rectangles must have sides of length 4 and 8.

Q: How do I identify corresponding sides in different orientations?

Look for the matching lengths! In both rectangles, find the sides that are 4 units long and the sides that are 8 units long. The orientation doesn't change these measurements.

Rectangle Congruence with Dimensional Arrangements

Are the rectangles below congruent?

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Understand the problem

Are the rectangles below congruent?

Step-by-step solution

Since there are two pairs of sides that are equal, they also have the same area:

$8\times4=32$

Therefore, the rectangles are congruent.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Congruence Rule: Same dimensions in different orientations create congruent rectangles
Area Check: Both rectangles have area $4 \times 8 = 32$
Verification: Compare all corresponding side lengths: 4=4 and 8=8 ✓

Common Mistakes

Avoid these frequent errors

Thinking rectangles must have same orientation to be congruent
Don't assume a 4×8 rectangle is different from an 8×4 rectangle = they're actually congruent! Orientation doesn't matter for congruence - only the dimensions. Always compare the actual side lengths, not their positions.

Practice Quiz

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Are the rectangles congruent?

FAQ

Everything you need to know about this question

How can rectangles with different orientations be congruent?

Congruent figures have the same size and shape, even if rotated! A 4×8 rectangle turned 90° becomes an 8×4 rectangle - they're still exactly the same rectangle.

Do I need to calculate the area to check congruence?

Not necessarily! While equal areas are a good sign, you should compare corresponding sides. Two shapes can have equal areas but different shapes (like a 2×16 and 4×8 rectangle).

What's the difference between congruent and similar rectangles?

Congruent rectangles are exactly the same size and shape. Similar rectangles have the same shape but can be different sizes. These 4×8 and 8×4 rectangles are congruent!

Would a 2×16 rectangle be congruent to these?

No! Even though $2 \times 16 = 32$ (same area), the sides are different lengths. For congruence, you need matching pairs of sides: both rectangles must have sides of length 4 and 8.

How do I identify corresponding sides in different orientations?

Look for the matching lengths! In both rectangles, find the sides that are 4 units long and the sides that are 8 units long. The orientation doesn't change these measurements.

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