# In triangle RST, RS = 10, RT = 15, and angle R = 32. In triangle UVW, UV=12, UW = 18, and angle U = 32. Are these polygons similar?

The corresponding sides are in the same ratio.

The triangles are similar.

Draw a sketch of the two triangles and fill in the given values. We have been given the lengths of corresponding sides. The combination is "two sides and the included angle in each case.

Are the given sides in the same ratio?

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Yes, these triangles are similar because they have the same angle measure (angle R = angle U = 32 degrees) and their corresponding sides are proportional (RS/UV = 10/12 = 5/6, RT/UW = 15/18 = 5/6).

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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.

- A triangle has corners points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #18 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #33 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #32 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #16 #, what is the length of side BC?
- Triangle A has sides of lengths #12 #, #9 #, and #6 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?
- Triangle A has an area of #24 # and two sides of lengths #8 # and #12 #. Triangle B is similar to triangle A and has a side with a length of #12 #. What are the maximum and minimum possible areas of triangle B?

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