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Q: Is a right-angle triangle has one angle of 90 o true or false?
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True or false Dilating a triangle changes the angles and side length of the triangle?

False.


Triangle with sides of lengths 20 21 and 29 is a right triangle true or false?

TRUE


AAA angle angle angle guarantees congruence between two triangles?

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True or false A triangle with sides of lengths 10 24 and 27 is a right triangle?

false In order for this to be a right triangle, the sum of the squares of the two shorter sides would have to equal the square of the longest side. 102=100 242= 576 272=729 102+242= 676, which does not equal 272=729, so a triangle with these lengths is not a right triangle.


True or false Two right triangles that are not similar still may have one congruent acute angle in common?

False. Assume that you had a two right triangles with one congruent acute (<90 degrees) angle in common. Let x represent the number of degrees in this angle in both triangles (which we can do since the angles are congruent). Let y represent the degree of the other angle in the first triangle and let z represent the degree of the other angle in the second triangle. We know that the sum of the degrees of the angles in a triangle is 180. So for the first triangle we have, 90+x+y = 180 For the second triangle, 90+x+z=180 Therefore, 90+x+y=90+x+z Subtract the 90+x from each side: y=z Therefore the degrees of the angles of the two triangles both are 90 [because they are both right triangles], x [because we said that this is the number of degrees of the congruent angles given in the problem], and y [because y=z]. Because the three angles of both triangles have the same measurement, the triangles must be similar.