Parallelograms of any form, a square, a rectangle, and a rhombus are just special parallelograms so all will form 2 pairs of isosceles triangles when a diagonal is drawn.
false
A decagon has 10 sides. To find the number of pairs of parallel diagonals in a decagon, we need to consider the possible combinations of diagonals that are parallel to each other. Each vertex can connect to 5 other vertices with a diagonal, but not all of these diagonals will be parallel. Therefore, the number of pairs of parallel diagonals in a decagon is 10 choose 2, which equals 45 pairs.
Correct. Congruency means that two triangles have three pairs of congruent angles and corresponding sides of the same lengths. A pair of triangles with three pairs of congruent angles but sides of different lengths are similar, not congruent.
This assumes you mean a regular octagon. There are 4 pairs where the diagonals each skip two vertices. Then there are 4 sets of three parallel diagonals where one is the main diagonal (skips three vertices) and two skip just one vertex. For each of these sets of three, you can choose three pairs of two. That makes 12 pairs all up. So there are 4 + 12 = 16 pairs.
The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.
No.
Four.
4
yes
False. There are 6 pairs of smaller congruent triangles and two pair of larger ones.
Probably 6 if not 4 if not 8 if not 10.WHO CARES
no theycan not
Pairs of triangles, in general, do not have to be similar.
4 congruent pairs
Yes. You can even have two triangles with two pairs of sides that are the SAME measure without the triangles being similar.
To prove that the sum of the angles formed by the intersection of the diagonals within a scalene pentagon equals 180 degrees, you can use the fact that any polygon can be divided into triangles. In a pentagon, there are five sides, and thus it can be divided into three triangles by drawing diagonals. The interior angles of these triangles sum to 540 degrees, and since the angles at the vertices of the pentagon contribute to this sum, the angles formed by the intersection of the diagonals can be shown to sum to 180 degrees by subtracting the angles at the vertices from 540 degrees and considering the properties of linear pairs.
false