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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.
