Math  /  Geometry

Questionming measures.
Consider the enlargement of the triangle.
Which statement is true about setting up a proportion to solve for the missing measure? Corresponding parts must be in different positions. Corresponding parts must be in the same position. The two ratios are not equal. The enlargement is not proportional to the original figure.

Studdy Solution

STEP 1

What is this asking? Which statement correctly describes how to set up a proportion to find the missing side length when a triangle is enlarged? Watch out! Don't mix up the corresponding sides of the triangles!
Make sure you're comparing apples to apples and oranges to oranges!

STEP 2

1. Understand Corresponding Sides
2. Analyze Proportion Statements

STEP 3

Alright, imagine we have two *similar* triangles, a small one and a big one, like a photo and its enlargement!
The corresponding sides are the sides that match up in the two triangles.
They're like the same side, just scaled up or down.

STEP 4

Think of it like this: the shortest side of the small triangle corresponds to the shortest side of the big triangle.
The longest side of the small triangle corresponds to the longest side of the big triangle, and so on.

STEP 5

Let's look at the first statement: "Corresponding parts must be in different positions." *Nope*.
This is incorrect.
We just talked about how corresponding sides *match up*!
They need to be in the *same* position in their respective ratios.

STEP 6

The second statement says, "Corresponding parts must be in the same position." *Bingo*!
This is exactly right.
When we set up a proportion, we need to make sure the corresponding sides are lined up.
For example, if we have small triangle side 1big triangle side 1\frac{\text{small triangle side 1}}{\text{big triangle side 1}}, then the other ratio *must* be small triangle side 2big triangle side 2\frac{\text{small triangle side 2}}{\text{big triangle side 2}}.

STEP 7

The third statement claims, "The two ratios are not equal." *False*!
If the triangles are similar (and they are, since it's an enlargement!), the ratios of corresponding sides *are* equal.
That's the whole point of proportions!

STEP 8

Lastly, we have "The enlargement is not proportional to the original figure." *Definitely not*!
An enlargement *is* proportional to the original figure.
That's what makes it an enlargement!
It's like multiplying the original by some factor.

STEP 9

The correct statement is: **Corresponding parts must be in the same position**.

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