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Math  /  Geometry

QuestionTriangle XYZX Y Z has side lengths 4, 10, and 12. Click and drag each transformation into one of the two boxes to classify them as producing a triangle similar to triangle XYZX Y Z or not similar to triangle XYZX Y Z.
Similar to Triangle XYZX Y Z Not Similar to Triangle XYZX Y Z
Add 10 to each side length. Subtract 1 from each side length. Multiply each side length by 4. Divide each side length by 3.

Studdy Solution

STEP 1

What is this asking? Which of these changes make a new triangle that's similar to the original triangle? Watch out! Similar triangles have the same angles, but not necessarily the same side lengths.
Changing the sides by adding, subtracting, multiplying, or dividing can affect whether the triangles are similar.

STEP 2

1. Check Multiplying
2. Check Dividing
3. Check Adding
4. Check Subtracting

STEP 3

When we **multiply** each side length by the **same number**, we create a similar triangle!
Think about blowing up a photo: it gets bigger, but it keeps the same shape.
Here, we're multiplying by **4**.
So, our new triangle has sides 4⋅4=164 \cdot 4 = 16, 10⋅4=4010 \cdot 4 = 40, and 12⋅4=4812 \cdot 4 = 48.
This new triangle *is* similar to the original triangle.

STEP 4

Dividing each side by the same number is just like multiplying by a fraction!
It's the same idea as shrinking a photo: it gets smaller, but it keeps the same shape.
Here, we're dividing by **3**.
Our new triangle has sides 4/34/3, 10/310/3, and 12/3=412/3=4.
This new triangle *is* similar to the original triangle.

STEP 5

Let's think about adding **10** to each side.
Our new triangle has sides 4+10=144 + 10 = 14, 10+10=2010 + 10 = 20, and 12+10=2212 + 10 = 22.
Imagine a triangle with sides 4, 10, and 12.
Now imagine adding 10 to each side.
Do you think the angles would stay the same?
Nope! Adding the same number to each side *doesn't* keep the proportions the same, so the triangles won't be similar.

STEP 6

Subtracting is just like adding a negative number.
Let's subtract **1** from each side.
Our new triangle would have sides 4−1=34 - 1 = 3, 10−1=910 - 1 = 9, and 12−1=1112 - 1 = 11.
Again, imagine a triangle, and now make each side a bit shorter.
The angles change!
So, subtracting the same number from each side *doesn't* keep the proportions the same, so the triangles won't be similar.

STEP 7

Multiplying each side length by 4 and dividing each side length by 3 result in similar triangles.
Adding 10 to each side length and subtracting 1 from each side length do *not* result in similar triangles.

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