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How many different isosceles triangles have at least one angle that measures exactly 20?
If one angle measures 20 degrees then the other two angles must each measure 80 degrees and many other similar or congruent isosceles triangles can have the same interior angles.
If two triangles are similar are they congruent?
no: if you have two triangles with the same angle measurements, but one has side lengths of 3in, 4in, and 5in and the other has side lengths of 6in, 8in, and 10in, then they are similar. Congruent triangles have the same angle measures AND side lengths.
If two triangles have equivalent angle measures then they are congruent?
If two triangles have equivalent angle measures, they are similar, but not necessarily congruent. Similar triangles have the same shape but can differ in size, meaning their corresponding sides are proportional, but not necessarily equal. Congruent triangles must have both equal angles and equal side lengths. Therefore, while equivalent angles imply similarity, they do not guarantee congruence.
What is a three sided polygons with the same shape but not the same size are called?
Three sided polygons would be triangles. Triangles that have the same shape (same angle measures) but are different sizes (different side lengths) would be called similar triangles. In similar triangles, corresponding sides have lengths in the same ratio. If triangle ABC is similar to triangle DEF, then: AB/DE = BC/EF = AC/DF.
Are two scalene triangles with congruent angles similar?
When all of their corresponding angles are congruent (in any triangle, in fact) then the triangles are similar. Similarity postulate AAA. (angle-angle-angle)
How many different isosceles triangles have at least one angle that measures exactly 20?
If one angle measures 20 degrees then the other two angles must each measure 80 degrees and many other similar or congruent isosceles triangles can have the same interior angles.
If two triangles are similar are they congruent?
no: if you have two triangles with the same angle measurements, but one has side lengths of 3in, 4in, and 5in and the other has side lengths of 6in, 8in, and 10in, then they are similar. Congruent triangles have the same angle measures AND side lengths.
What is a three sided polygons with the same shape but not the same size are called?
Three sided polygons would be triangles. Triangles that have the same shape (same angle measures) but are different sizes (different side lengths) would be called similar triangles. In similar triangles, corresponding sides have lengths in the same ratio. If triangle ABC is similar to triangle DEF, then: AB/DE = BC/EF = AC/DF.
Is angle angle angle a way to show that triangles are similar?
Yes, AAA is a way to show that triangles are similar. Note, however, that AAA is not a way to show that triangles are congruent.
If an angle bisector of an isosceles triangle yields two isosceles triangles what were the angle measures of the original triangle?
they would be congruent triangles!
How do you prove triangles similar?
To prove that two or more triangles are similar, you must know either SSS, SAS, AAA or ASA. That is, Side-Side-Side, Side-Angle-Side, Angle-Angle-Angle or Angle-Side-Angle. If the sides are proportionate and the angles are equal in any of these four patterns, then the triangles are similar.
Are two scalene triangles with congruent angles similar?
When all of their corresponding angles are congruent (in any triangle, in fact) then the triangles are similar. Similarity postulate AAA. (angle-angle-angle)
How you can prove that the angles of two triangles are equal?
If the angles of two triangles are equal the triangles are similar. AAA If you have three angles on both triangles these must be equal for the triangles to be similar. SAS If you have an angle between two sides and the length of the sides and the angle are the same on both triangles, then the triangles are similar. And SSS If you know the three sides
Can two triangles be congruent if all three angles have exactly the same measures?
No, they cannot, because if you think about it, the sides can be different proportional lengths but have the same angle measures.
Are the three angle measures always generate a unique triangle?
Yes, three angle measures always generate a unique triangle, provided that the angles sum to 180 degrees. This is based on the Angle-Angle-Angle (AAA) similarity postulate, which states that if two triangles have the same angle measures, they are similar. However, the triangles can only be considered unique in the sense of their shape; they can vary in size based on a scale factor. Therefore, while the angles determine the shape, they do not uniquely define a specific triangle in terms of size.
If triangle has a 30 degree angle and an angle that measures twice this amount what is the measure of the triangles third angle?
90 degrees
Can two triangles be similar but not congruent?
Yes. The triangles have the same angle measures but different, similar side lengths. Think of two different sized equilateral triangles. One can have side lengths of 6 inches while the other has side lengths of 20 inches, but they still have congruent angles of 60 degrees. Each ratio of side lengths is equal [6/20=6/20=6/20].
