# If I have two triangles, and they are similar but different sizes, how would I write a similarity statement for them?

Let the 2 similar triangles have vertices A,B,C and D,E,F respectively.

Then we write :

When 2 triangles are similar, then all their corresponding angles are equal, and all their corresponding sides are in proportion.

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If two triangles are similar but different in size, you can write a similarity statement by identifying the corresponding angles and sides.

For example, if triangle ABC is similar to triangle DEF, you can write the similarity statement as:

Triangle ABC ~ Triangle DEF

You can also specify the corresponding vertices, indicating which angles and sides correspond:

∠A ≅ ∠D ∠B ≅ ∠E ∠C ≅ ∠F

And you can denote the corresponding sides:

AB/DE = BC/EF = AC/DF

This statement asserts that the corresponding angles are congruent and the corresponding sides are proportional, indicating similarity between the two triangles.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Triangle A has an area of #12 # and two sides of lengths #5 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #19 #. What are the maximum and minimum possible areas of triangle B?
- Triangle A has an area of #9 # and two sides of lengths #4 # and #6 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the maximum and minimum possible areas of triangle B?
- Triangle A has sides of lengths #35 #, #25 #, and #48 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?
- A triangle has corners at points A, B, and C. Side AB has a length of #42 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #45 #, what is the length of side BC?
- Triangle A has sides of lengths #36 #, #44 #, and #32 #. Triangle B is similar to triangle A and has a side of length #4 #. What are the possible lengths of the other two sides of triangle B?

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