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If an acute angle of one right triangle is congruent to an angle of a second triangle then are the triangles similar?
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∙ 14y ago
true.
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∙ 14y ago
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Mathematics similarities of triangles?
Two triangles are considered to be similar if for each angles in one triangle, there is a congruent angle in the other triangle.Two triangles ABC and A'B'C' are similar if the three angles of the first triangle are congruent to the corresponding three angles of the second triangle and the lengths of their corresponding sides are proportional as follows: AB / A'B' = BC / B'C' = CA / C'A'
What is triangular theorem SSS?
If three sides of one triangle are congruent tothree sides of a second triangle, then the three triangles are congruent.
What states that if the sides of one triangle are congruent to the sides of a second triangle then the triangles are congruent?
It is a congruence theorem. There are several of them and they are not all numbered the same way.
What is the meaning of AAA Similarity Theorem?
If three angles of one triangle are congruent to three angles of another triangle then by the AAA similarity theorem, the two triangles are similar. Actually, you need only two angles of one triangle being congruent to two angle of the second triangle.
The sum of the perimeters of two congruent triangles is three times the perimeter of the first triangle?
Let's denote the perimeter of the first triangle as P. Since the triangles are congruent, the perimeter of the second triangle is also P. The sum of their perimeters is then 2P. According to the given statement, this sum is three times the perimeter of the first triangle. So we have the equation 2P = 3P. Simplifying, we find that P = 0, which is not a valid solution. Therefore, there is no triangle for which the sum of the perimeters of two congruent triangles is three times the perimeter of the first triangle.
Mathematics similarities of triangles?
Two triangles are considered to be similar if for each angles in one triangle, there is a congruent angle in the other triangle.Two triangles ABC and A'B'C' are similar if the three angles of the first triangle are congruent to the corresponding three angles of the second triangle and the lengths of their corresponding sides are proportional as follows: AB / A'B' = BC / B'C' = CA / C'A'
If two sides of one triangle are proportional to two sides of a second triangle and the included angles of those sides are congruent then are the triangles similar?
If the 3 sides are proportional by ratio and the angles remain the same then the two triangles are similar
The SSS Postulate states that if the sides of one triangle are congruent to the sides of a second triangle then the triangles are congruent?
Yes, it does.
What is triangular theorem SSS?
If three sides of one triangle are congruent tothree sides of a second triangle, then the three triangles are congruent.
What states that if the sides of one triangle are congruent to the sides of a second triangle then the triangles are congruent?
It is a congruence theorem. There are several of them and they are not all numbered the same way.
What is the meaning of AAA Similarity Theorem?
If three angles of one triangle are congruent to three angles of another triangle then by the AAA similarity theorem, the two triangles are similar. Actually, you need only two angles of one triangle being congruent to two angle of the second triangle.
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle then the two triangles are congruent This is known as what?
SAS
What does side angle side mean?
side angle side means if two sides in their included angle in one triangle are congruent to the corisponding parts of the second triangle then the triangles are congruent so only if they are congruent. i need it for a classs...
The sum of the perimeters of two congruent triangles is three times the perimeter of the first triangle?
Let's denote the perimeter of the first triangle as P. Since the triangles are congruent, the perimeter of the second triangle is also P. The sum of their perimeters is then 2P. According to the given statement, this sum is three times the perimeter of the first triangle. So we have the equation 2P = 3P. Simplifying, we find that P = 0, which is not a valid solution. Therefore, there is no triangle for which the sum of the perimeters of two congruent triangles is three times the perimeter of the first triangle.
What is the angle-angle-side rule?
Side-Angle-Side is a rule used in geometry to prove triangles congruent. The rule states that if two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. An included angle is an angle created by two sides of a triangle.
Can two triangles be congruent with 5 pairs of congruent parts?
Two triangles are congruent if the six elements of one triangle (three sides and three angles) are equal to the six elements of the second triangle and the two triangles have a scale factor of 1. However, in four special cases it is only necessary to match three elements to prove that two triangles are congruent. The matching of four elements is sometimes necessary, and the matching of five elements would put the matter beyond any doubt.
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.
