Rectangle Similarity: Compare ABCD (7x3) with EFGH (10x6)

Q: Why can't I just compare the lengths directly?

Similar shapes require proportional sides, not just bigger or smaller measurements. You must check if the ratios are equal: $ \frac{\text{length}_1}{\text{length}_2} = \frac{\text{width}_1}{\text{width}_2} $

Q: How do I identify corresponding sides in rectangles?

In rectangles, lengths correspond to lengths and widths correspond to widths. Look at the diagram: 7 and 10 are lengths, while 3 and 6 are widths.

Q: What if one ratio is a fraction I can't simplify easily?

Convert both ratios to decimal form or find a common denominator. For example: $ \frac{7}{10} = 0.7 $ and $ \frac{3}{6} = 0.5 $, so they're clearly not equal.

Q: Can rectangles be similar if they have different orientations?

Yes! Orientation doesn't matter for similarity. What matters is whether the ratio of length to width is the same in both rectangles, regardless of which side is horizontal or vertical.

Q: If the ratios were equal, what would that mean?

If $ \frac{7}{10} = \frac{3}{6} $, then rectangle ABCD would be a scaled version of rectangle EFGH. All angles would be the same (90°) and corresponding sides would be proportional.

Rectangle Similarity with Ratio Verification

Is rectangle ABCD similar to rectangle EFGH?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Are the rectangles similar?

00:03 Let's check the ratio of the sides

00:07 If the similarity ratio is equal, then the rectangles are similar

00:15 Let's substitute appropriate values and solve to find the ratio

00:28 The ratios are not equal, therefore the rectangles are not similar

00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Is rectangle ABCD similar to rectangle EFGH?

Step-by-step solution

We first need to verify the ratio of similarity.

We examine if:

$\frac{AB}{EF}=\frac{AC}{EG}$

To do this, we substitute our values in:

$\frac{7}{10}=\frac{3}{6}$

$\frac{7}{10}\ne\frac{1}{2}$

The ratio is not equal, therefore the rectangles are not similar.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Similar rectangles must have equal ratios of corresponding sides
Technique: Compare ratios: $\frac{7}{10}$ versus $\frac{3}{6} = \frac{1}{2}$
Check: If ratios are unequal, rectangles cannot be similar ✓

Common Mistakes

Avoid these frequent errors

Comparing lengths without checking ratios
Don't just compare individual measurements like 7 vs 10 or 3 vs 6 = incorrect conclusion! This ignores the proportional relationship needed for similarity. Always compare the ratios of corresponding sides to determine similarity.

Practice Quiz

Test your knowledge with interactive questions

Is the similarity ratio between the three triangles equal to one?

FAQ

Everything you need to know about this question

Why can't I just compare the lengths directly?

Similar shapes require proportional sides, not just bigger or smaller measurements. You must check if the ratios are equal: $\frac{\text{length}_1}{\text{length}_2} = \frac{\text{width}_1}{\text{width}_2}$

How do I identify corresponding sides in rectangles?

In rectangles, lengths correspond to lengths and widths correspond to widths. Look at the diagram: 7 and 10 are lengths, while 3 and 6 are widths.

What if one ratio is a fraction I can't simplify easily?

Convert both ratios to decimal form or find a common denominator. For example: $\frac{7}{10} = 0.7$ and $\frac{3}{6} = 0.5$ , so they're clearly not equal.

Can rectangles be similar if they have different orientations?

Yes! Orientation doesn't matter for similarity. What matters is whether the ratio of length to width is the same in both rectangles, regardless of which side is horizontal or vertical.

If the ratios were equal, what would that mean?

If $\frac{7}{10} = \frac{3}{6}$ , then rectangle ABCD would be a scaled version of rectangle EFGH. All angles would be the same (90°) and corresponding sides would be proportional.

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