Similar Triangles: Calculate Length FE Using 8y and 7m Measurements

Q: How do I know which sides correspond to each other?

Look at the order of the triangle names! Triangle ABC ~ Triangle DFE means the first letters match (A↔D), second letters match (B↔F), and third letters match (C↔E). So AB corresponds to DF, BC to FE, and AC to DE.

Q: Why can I cancel out the y in the proportion?

Since both 8y and 9y have the same variable y, you can divide both by y to get $ \frac{8}{9} $. This simplifies the calculation without changing the ratio!

Q: How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $ \frac{63}{8} = 7\frac{7}{8} $ because 63 ÷ 8 = 7 remainder 7. The quotient becomes the whole number and the remainder becomes the new numerator.

Q: What if the triangles were named in different order?

Always check the diagram carefully! The problem states which triangle is similar to which. Match corresponding angles and sides based on position, not just alphabetical order.

Proportional Reasoning with Mixed Number Results

Triangle DFE is similar to triangle ABC.

Calculate the length of FE.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find FE

00:03 The triangles are similar according to the given data

00:15 Find the similarity ratio

00:30 Substitute appropriate values and solve for FE

00:42 Simplify what we can

00:47 Isolate FE

00:56 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

Triangle DFE is similar to triangle ABC.

Calculate the length of FE.

Step-by-step solution

Let's look at the order of letters of the triangles that match each other and see the ratio of the sides.

We will write accordingly:

Triangle ABC is similar to triangle DFE

The order of similarity ratio will be:

$\frac{AB}{DF}=\frac{BC}{FE}=\frac{AC}{DE}$

Now let's insert the existing data we have in the diagram:

$\frac{8y}{9y}=\frac{7m}{FE}$

Let's reduce y and we get:

$\frac{8}{9}FE=7m$

$FE=\frac{9}{8}\times7m$

$FE=7\frac{7}{8}m$

Final Answer

$7\frac{7}{8}m$

Key Points to Remember

Essential concepts to master this topic

Similarity Rule: Corresponding sides of similar triangles are proportional
Technique: Set up ratio $\frac{8y}{9y} = \frac{7m}{FE}$ and cross-multiply
Check: Verify $\frac{8}{9} \times 7\frac{7}{8}m = 7m$ ✓

Common Mistakes

Avoid these frequent errors

Setting up incorrect correspondence between triangles
Don't match sides randomly like AB with DE instead of DF = wrong proportions! This happens when you don't carefully identify which vertices correspond to each other in similar triangles. Always write the triangle names in corresponding order: ABC ~ DFE means A↔D, B↔F, C↔E.

Practice Quiz

Test your knowledge with interactive questions

If it is known that both triangles are equilateral, are they therefore similar?

FAQ

Everything you need to know about this question

How do I know which sides correspond to each other?

Look at the order of the triangle names! Triangle ABC ~ Triangle DFE means the first letters match (A↔D), second letters match (B↔F), and third letters match (C↔E). So AB corresponds to DF, BC to FE, and AC to DE.

Why can I cancel out the y in the proportion?

Since both 8y and 9y have the same variable y, you can divide both by y to get $\frac{8}{9}$ . This simplifies the calculation without changing the ratio!

How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $\frac{63}{8} = 7\frac{7}{8}$ because 63 ÷ 8 = 7 remainder 7. The quotient becomes the whole number and the remainder becomes the new numerator.

What if the triangles were named in different order?

Always check the diagram carefully! The problem states which triangle is similar to which. Match corresponding angles and sides based on position, not just alphabetical order.

Can I solve this without cross-multiplying?

Yes! You can also multiply both sides by FE, then divide by $\frac{8}{9}$ (which is the same as multiplying by $\frac{9}{8}$ ). Both methods give the same answer.

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