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In similar triangles, the corresponding angles are indeed congruent, meaning that each angle in one triangle matches in measure with an angle in the other triangle. This property arises from the fact that similar triangles maintain the same shape, even if their sizes differ. Consequently, the ratios of the lengths of corresponding sides are equal, reinforcing the relationship between the angles. This congruence of angles is a fundamental characteristic that helps identify and prove the similarity of triangles.
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If the corresponding side lengths of two triangles are congruent the corresponding angles are also congruent.?
False. The statement should be: If the corresponding side lengths of two triangles are congruent, and the triangles are similar, then the corresponding angles are also congruent.
Similar triangles are triangles whose corresponding angles are congruent and whose corresponding sides are in length?
proportional
What are the corresponding sides called in similar triangles whose corresponding angles are congruent?
Proportional.
What is two triangles with corresponding angles and corresponding sides congruent called?
They are congruent triangles.
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)
If the corresponding side lengths of two triangles are congruent the corresponding angles are also congruent.?
False. The statement should be: If the corresponding side lengths of two triangles are congruent, and the triangles are similar, then the corresponding angles are also congruent.
Are corresponding angles of similar triangles congruent?
Yes.
Are two triangles with corresponding congruent angles congruent?
No, they are similar. They may be congruent, but they need not be.
Can you assume that corresponding sides and corresponding angles of any two similar triangles are congruent and why?
you can assume that the angles are congruent, but not the sides.
Similar triangles are triangles whose corresponding are congruent and whose corresponding sides are proportional in length?
angles
Similar triangles are triangles whose corresponding angles are congruent and whose corresponding sides are in length?
proportional
What are the corresponding sides called in similar triangles whose corresponding angles are congruent?
Proportional.
What is two triangles with corresponding angles and corresponding sides congruent called?
They are congruent triangles.
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)
Triangles are congruent if they have the same what?
Triangles are congruent if the lengths of their corresponding sides as well as the measures of their corresponding angles are the same.
Similar triangles are triangles whose corresponding?
angles are congruent. That is sufficient to force the corresponding sides to be proportional - which is the other definition of similarity.
What are the two properties of congruent triangles?
All the corresponding sides in congruent triangles are equal All the corresponding angles in congruent triangles are equal
