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Each has 3 interior angles of 60 degrees
Each has 3 equal sides in length
Similar triangles are defined as those that have corresponding angles of the same measure.
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To construct a perpendicular bisector to a given line segment one must construct two?
Equilateral triangles
If triangle ABC is congruent to triangle bcd then triangles ABC and bcd are what kinds of triangles?
The 2 triangles can be of any type (e.g isosceles, equilateral, etc.), only they must be exactly the same if they are congruent, i.e one triangle must be an exact copy of the other one.
Are congruent triangles similar?
Yes, similar triangles are congruent because in order to be congruent they must first be equal. Which in turn is the definition of a similar triangle. A triangle equal in angle measurements and/or side lengths. So, yes.
Are similar triangles always congruent?
No, congruent triangles are always similar but similar triangles and not always congruent. Imagine that similar triangles can be created on a copy machine enlarge and shrink the image, turn it, even turn it over, the angles remain the same. A congruent triangle must be exactly the same as the original. Hope this helps!
Can any two triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
Are two equilateral triangles sometimes always or never similar to each other?
Since triangles have three sides and must have interior angles equal to pi or 180o, the three interior angles in all equilateral triangles will be pi/3 or 60o.However, equilateral triangles must also have equal side lengths. Since equilateral triangles with interior angles of 60o will not necessarily have the same side lengths, two equilateral triangles will sometimes be similar to each other.
Equilateral triangles must also be?
equiangular.
Which pair of triangles must be similar?
Pairs of triangles, in general, do not have to be similar.
When is an equilateral triangle not equiangular?
If a triangle is equiangular, it will have all equal angles. So, it might be similar to another equiangular triangle, but not congruent. It is not equilateral if the sides are not equal in length. All equiangular triangles are similar, but not all of them are congruent, which means they do not all have corresponding side lengths. But, all equilateral triangles are equiangular.
Every equilateral triangle must also be an acute triangle?
Equilateral triangles have angles that all equal 60 degrees. Acute triangles all have an angles that are less than 90 degrees.
Is it true that when equilateral triangles have equal perimeters they must also have equal areas?
Yes.
Are all equalateral triangles isosceles?
Yes. All equilateral triangles have three equal sides (or angles) so two of them MUST be equal.
Does an equilateral triangle have line symmetry?
In order to have any lines of symmetry, a triangle must have either two sides equal (isosceles) or three sides equal (equilateral).
To construct a perpendicular bisector to a given line segment one must construct two?
Equilateral triangles
An equilateral triangle is a right triangle?
Never. All equilateral triangles have equal angles, which means every angle must be 60 degrees and therefore not right.
How many 1 inch triangles are needed to make a row of triangles that has a perimeter of 20 inches?
If a "1 inch triangle" means a triangle each of whose sides is 1 inch, then there is no answer to the question. These are equilateral triangles and equilateral triangles can tesselate to form a larger equilateral triangle. The fact that the large triangle is equilateral means that its three sides are equal so that its perimeter ie the sum of the three sides must be divisible by 3. 20 is not divisible by 3.
Are all right triangles equilateral triangles?
no. In fact a right angled triangle cannot be equilateral. An equilateral triangle is also equiangular: that is, all its angles are equal. The sum of all three angles of a [plane] triangle must be 180 degrees and so they cannot be 90 deg each.
