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- SSS - Side-Side-Side
- AAS - Angle-Angle-Side; ASA - Angle-Side-Angle
- SAS - Side-Angle-Side
Note: it is important that the angle is the one between the corresponding sides of equal length.
- RHS - Right_angle-Hypotenuse-Side
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Does an acute triangle have two congruent sides?
Not every acute triangle has two congruent sides, although some do, in which case they are called isosceles triangles.
When do you say that two triangles have the same shape?
well, they could be congruent, there are some rules for congruency, to be congruent two triangles have, ASA-two angles the same with a side length between them. SAS-two side lengths the same and a same angle between them. SSS-all 3 side lengths the same. RHS-if the triangles are right angles ,and the hypotenuse are the same. ;or they could be mathmatically similar. :)
Are some isosceles triangles equilateral triangles?
All isosceles triangles are not equilateral triangles
What are some special right triangles?
your mom is the right triangles
Are some right triangles also the same as equilateral triangles?
No...
Does a triangle have 2 congruent sides?
Some, but not all. Triangles with 2 congruent sides are called isoceles triangles. Triangles with 3 congruent sides are called equilateral triangles.
Are some scalene triangles isosceles?
never scalene-0 sides congruent isoceles-2 sides congruent
Which theorem is used to prove the AAS triangle congruence postulate theorem?
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way). You just need to show AAS is equivalent or implies SSS and you are done. That's the first theorem I thought of, don't know if it works though, not a geometry major.
What does CPCTE stand for in geometry?
Corresponding parts of congruent triangles are congruent, perhaps some people use equal instead of congruent?
Why congruence is a special case of similarity?
Term similar is more wide than term congruent. For example: if you say that two triangles are congruent that automatically means that they are similar, but if you say that some two triangles are similar it doesn't have to mean that they are congruent.
Does an acute triangle have two congruent sides?
Not every acute triangle has two congruent sides, although some do, in which case they are called isosceles triangles.
How can you used a triangle to prove quadrilateral is a parallelogram?
A quadrilateral, in general, is not a parallelogram. If it is a parallelogram then you will have some additional information about its sides and angles. If you do not have such information it is not possible to prove that it is a parallelogram. Draw a diagonal which will divide the quadrilateral into two triangles and use the additional information that you have to show that the triangles are congruent. This can then be used to show equality of sides or of angles: the latter can then be used to show that sides are parallel. Note that the choice of which diagonal may influence how (if at all) you proceed.
What is congruent angle?
Congruent angles are of the same size as for example 85 degrees is congruent to 85 degrees
Is a right angle an isosceles angle?
Isosceles triangles are triangles in which 2 angles and 2 sides are congruent, or equal. There is nothing called an isosceles angle. Some isosceles triangles are right triangles. This is where the non-congruent triangle is a right triangle, and the other two are 45 degrees each. This type of triangle is called a 45-45-90 triangle. Two sides are multiples of one and the third is a multiple of root-2. In other words yes it is.
When do you say that two triangles have the same shape?
well, they could be congruent, there are some rules for congruency, to be congruent two triangles have, ASA-two angles the same with a side length between them. SAS-two side lengths the same and a same angle between them. SSS-all 3 side lengths the same. RHS-if the triangles are right angles ,and the hypotenuse are the same. ;or they could be mathmatically similar. :)
When are two triangles said to be congruent?
Congruent means the same size and shape. Two triangles are congruent if the 3 sides and 3 angles of one are equal to the respective sides and angles, in order, of the other. Thus the triangles ABC and DEF are congruent if the lengths of AB and DE are equal, as well as BC and EF, and CA and FD, and the angle at A equals the angle at D, likewise that at B and at E, and of course if those two are true, the angle at C must equal the one at F since the 3 angles in a triangle always add up to 180 degrees. Two triangles are congruent if you can rigidly move one to exactly coincide with the other. It might be necessary to rotate it through 3-dimensional space, if the triangles are mirror images of each other. There are some theorems that give criteria that guarantee triangles to be congruent. One is side-side-side, abbreviated SSS, meaning that if the sides of two triangles, in order, are equal, so are the angles. Another is SAS, meaning two sides of one triangle and the angle included between them are equal to the corresponding parts of the other. If 2 of the angles of two triangles are the same (AA), so is the third, and the triangles are similar (same shape, but not necessarily the same size). Then all you need is that one side and the corresponding side in the other triangle are equal to prove congruence. There is one ambiguous case: SSA. Depending on the length of the side opposite the given angle, there may be 0, 1, or 2 different (non-congruent) triangles having the given part measures: 0 if the side is too short, 1 if it is the length of the perpendicular to the other side, and 2 if it is longer than that. Answer 1 ======= When they both have the same 3 interior angles and the same length of sides
How many congruent sides does an equilateral have?
Equilateral triangles have 3 congruent(equal) sides and 3 congruent angles, because equilateral means that all the sides are equal. If a polygon(shape with 3 + sides) is equilateral and equiangular( all the angles are the same), then it is regular. Some equiangular polygons are not equilateral, and vice versa.
