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Two right triangles that are not similar can still have a pair of congruent acute angles.A.TrueB.FalseSUBMITarrow_backPREVIOUS

Question

Two right triangles that are not similar can still have a pair of congruent acute angles.

A. True
B. False

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Solution

Break Down the Problem

  1. Determine the properties of right triangles, particularly the angles.
  2. Assess whether two right triangles can have congruent acute angles while being non-similar.

Relevant Concepts

  1. The angles in a right triangle consist of one right angle (90 degrees) and two acute angles.
  2. In any triangle, the sum of the angles is always 180 degrees.
  3. Two triangles are similar if they have the same shape, which is true if corresponding angles are equal.

Analysis and Detail

  1. For right triangles, there are two acute angles, denoted as A A and B B .
  2. Since A+B+90=180 A + B + 90^\circ = 180^\circ , it follows that A+B=90 A + B = 90^\circ .
  3. If two right triangles have a pair of congruent acute angles, let’s say A A , then the other acute angle B B will be dependent on A A (as B=90A B = 90^\circ - A ).
  4. If both triangles have one acute angle equal, then the remaining angles must also sum to 90 degrees in both triangles. This means the triangles would indeed be similar, as they would have the same angle configuration.

Verify and Summarize

If two right triangles have a pair of congruent acute angles, they must share the same two acute angles; thus, they are similar triangles. Therefore, the statement asserting that two non-similar right triangles can have a pair of congruent acute angles is false.

Final Answer

B. False

This problem has been solved

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