# If two triangles are congruent, are they similar? Please explain why or why not.

Yes, they are similar.

For two triangles to be similar, it is sufficient if two angles of one triangle are equal to two angles of the other triangle. Note that if two angles of one are equal to two angles of the other triangle, the tird angles of the two triangles too will be equal.

If two triangles are congruent then all corresponding sides as well as corresponding angles of one triangle are equal to those of other triangles. This can happen in four cases

Observe that for triangles to be similar, we just need all angles to be equal. But for triangles to be cogruent, angles as well as sides sholud be equal.

Hence, while congruent triangles are similar, similar triangles may not be congruent.

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If two triangles are congruent, then they are similar. This is because congruent triangles have exactly the same shape and size, which implies that all corresponding angles are equal, and all corresponding sides are equal in length. In turn, this satisfies the criteria for similarity, where corresponding angles are equal, and corresponding sides are proportional. Therefore, if two triangles are congruent, they must also be similar.

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No, if two triangles are congruent, they are not necessarily similar. Congruent triangles have exactly the same shape and size, meaning all corresponding sides and angles are equal. Similar triangles, on the other hand, have the same shape but not necessarily the same size. They have corresponding angles that are equal, but their corresponding sides are proportional, meaning they have the same ratio.

In summary, while congruent triangles are always similar, similar triangles are not always congruent.

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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 at points A, B, and C. Side AB has a length of #56 #. 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 #42 #, what is the length of side BC?
- Triangle A has an area of #5 # and two sides of lengths #9 # and #12 #. Triangle B is similar to triangle A and has a side with a length of #25 #. What are the maximum and minimum possible areas of triangle B?
- Triangle A has an area of #15 # and two sides of lengths #6 # and #7 #. 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?
- A triangle has corners at 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 #7 #. If side AC has a length of #21 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #16 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #32 #, what is the length of side BC?

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