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The correct statements about similarity of triangles are A, B, and C.

What is a similar triangle?

Similar triangles are triangles that have the same shape, but their sizes may vary. This type of triangles are said to have congruent angles and corresponding sides.

From the given figure,

  • triangle ABC is a right triangle and triangle BDC is also a right triangle
  • triangle ABC is a right triangle and triangle ADB is also a right triangle
  • angle ABD is 45 and angle BCD is also 45 degrees.

Thus, the correct statements about similarity of triangles are A, B, and C.

Learn more about similar triangles here: https://brainly.com/question/2644832

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Answer:

  A, B, C

Step-by-step explanation:

In this figure, all of the right triangles are similar, easily shown using the AA similarity postulate. The idea here is to correctly identify the names of the similar triangles. We can do that by naming the triangles this way:

  shortest side - right angle vertex - longest side

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similar triangles

Starting with the largest triangle, and working toward the smallest, we can identify the similar triangles as ...

  ΔABC ~ ΔBDC ~ ΔADB

From this statement, we can readily match choices A and B.

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different order

If we reorder the last two vertices in each similarity statement above, we get ...

  ΔACB ~ ΔBCD ~ ΔABD

We can match the last part of this similarity statement to choice C.

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We note that points A, D, C are collinear, so do not form a triangle. This eliminates choice D.

  Similarity statements A, B, and C are true.

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