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Why are triangles congruent that have three sides but the same is not true for triangles that have the same three angles?
The same three sides also determine the angles uniquely. However, the same three angles do not uniquely determine the sides: they only determine the ratio between the sides. So, two triangles with the same angles can be of different size (similar triangles).
If two triangles are similar statements are true?
If two triangles are similar, their corresponding angles are equal, and their corresponding sides are proportional. This means that the ratio of the lengths of any two corresponding sides is the same for both triangles. Additionally, the area ratio of the triangles is equal to the square of the ratio of their corresponding side lengths.
What is true about triangles that are congruent?
All 3 angles and all 3 sides are the same
Is it true that two triangles have 3 pairs of congruent angles then the triangle are not guaranteed to be congruent?
When two triangles are congruent, there are 6 facts that are true about the triangles. The triangles have 3 sets of congruent (of equal length) sides and the triangles have 3 sets of congruent (of equal measure) angles.
What statements are true about two triangles that are congruent?
Their 3 sides and 3 interior angles will be identical
What is true about corresponding angles and corresponding sides of similar figures?
The ratio between corresponding sides or angles of similar triangles are equal
Why are triangles congruent that have three sides but the same is not true for triangles that have the same three angles?
The same three sides also determine the angles uniquely. However, the same three angles do not uniquely determine the sides: they only determine the ratio between the sides. So, two triangles with the same angles can be of different size (similar triangles).
With similar triangles the corresponding angles are equal True or False?
True. With similar triangles the corresponding angles are equal.
Are all equilateral triangles are congruent?
no. if one triangles sides are all 2 and one triangles sides are all 3 then they are not congruent
If two triangles are similar statements are true?
If two triangles are similar, their corresponding angles are equal, and their corresponding sides are proportional. This means that the ratio of the lengths of any two corresponding sides is the same for both triangles. Additionally, the area ratio of the triangles is equal to the square of the ratio of their corresponding side lengths.
Is this statement true or false corresponding sides of similar triangles have the same measure?
False because although the angles are the same the sides are proportional by ratio to each other.
What is true about triangles that are congruent?
All 3 angles and all 3 sides are the same
Is it true that two triangles have 3 pairs of congruent angles then the triangle are not guaranteed to be congruent?
When two triangles are congruent, there are 6 facts that are true about the triangles. The triangles have 3 sets of congruent (of equal length) sides and the triangles have 3 sets of congruent (of equal measure) angles.
Is it true that triangles are congruent if they have the same size?
Yes providing they have the same sides and same angles
What statements are true about two triangles that are congruent?
Their 3 sides and 3 interior angles will be identical
True or false Similar polygons have congruent sides and congruent angles?
False. The angles will be congruent, but the sides not so.
If two triangles have three pairs of congruent angles then the triangles are guaranteed to be congruent true or false?
False, because they could be similar triangles having the same angles but proportionally different side lengths
