# Given points #M(0, 10)#, #N(5, 0)# and #P(15, 15)# in #DeltaMNP# and points #M(0, 10)#, #Q(10, -10)#, and #R(30, 20)# in #DeltaMQR#, how do we find that the two triangles are similar?

Find all the sides and check whether they are proportional.

and as sides of two triangles are proportional, we have

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We can determine if two triangles are similar by checking if their corresponding angles are congruent and their corresponding sides are proportional. In this case, we can compare the ratios of the lengths of the sides of DeltaMNP to the lengths of the sides of DeltaMQR. If the ratios are equal, then the triangles are similar. We can use the distance formula to calculate the lengths of the sides and then compare the ratios. If the ratios of the corresponding sides are equal, and the corresponding angles are congruent, then the triangles are similar.

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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 sides of lengths #15 #, #12 #, and #12 #. 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?
- A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #24 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #44 #. The distance between the intersection of point A's angle bisector with side BC and point B is #24 #. If side AC has a length of #32 #, what is the length of side BC?
- Yosief is 4 feet 9 inch boy. He stands in front of a tree and sees that it's shadow coincide with his. Yosief shadow measures 9 feet 6 inches. Yosief measures the distance between him and the tree to calculate its height, how does he do it?
- 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 #6 #. If side AC has a length of #18 #, what is the length of side BC?

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