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How are parallelogram related to triangles and rectangles?
If you draw one diagonal across a parallelogram, it will split it into two congruent triangles. A rectangle is a parallelogram, with all four angles equal to 90°.
Does the diagonals of a parallelogram bisect the angles?
No, the diagonals of a parallelogram do not necessarily bisect the angles. The diagonals of a parallelogram divide it into four congruent triangles, but they do not necessarily bisect the angles of those triangles.
Does A diagonal of parallelogram intersects all four sides?
Yes: The intersection is at one end of each side. This is true for a diagonal of any quadrilateral.
Does a parellelogram have four congruent triangles?
Yes. Read on for why: Take a parallelogram ABCD with midpoints E and F in the bases. So something like this (forgive the "drawing"): A E B __.__ /__.__/ C F D We know that parallelogram AEFC = EBDF, since they have the same base (F bisects CD, so CF = FD), height (haven't touched that), and angles (<ACF = <EFD because they're parallel - trust me that everything else matches). We also know that every parallelogram can be divided into two congruent triangles along their diagonal. So if two congruent parallelograms consistent of two congruent triangles each, then all four triangles are congruent. So your congruent triangles are ACF, AEF, EFD, and EBD. You can further reinforce this through ASA triangle congruency proofs (as I did at first), but this is a far more concise and equally valid answer.
What quadrilateral can have a diagonal line and is made with 2 equilateral triangles?
A Rhombus. If it makes two equilateral triangles with a diagonal, the shape must have all four sides of equal length; thus it is a rhombus, possibly a square. As an equilateral triangle is made, the angle between two of the sides is 60o; which is not 90o, so it can't be a square, so it must be a rhombus.
How are parallelogram related to triangles and rectangles?
If you draw one diagonal across a parallelogram, it will split it into two congruent triangles. A rectangle is a parallelogram, with all four angles equal to 90°.
What is Jamaicas national flag?
A diagonal yellow cross which divides the flag into four triangles with the hoist and outer side colored black and the upper and lower triangles in green.
If you have 8 small triangles made of 16 lines how can you make four small triangles if it is a parallelogram?
If you have 8 small triangles made of 16 lines how can you make four small triangles if it is a parallelogram?
Can a parallelogram be separated into four triangles?
Yes
The point at which the diagonal of a parallelogram intersect is equidistant from the four vertices?
sometimes
Does the diagonals of a parallelogram bisect the angles?
No, the diagonals of a parallelogram do not necessarily bisect the angles. The diagonals of a parallelogram divide it into four congruent triangles, but they do not necessarily bisect the angles of those triangles.
What shape can you make using four equilateral triangles?
A parallelogram.
Does A diagonal of parallelogram intersects all four sides?
Yes: The intersection is at one end of each side. This is true for a diagonal of any quadrilateral.
Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?
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.
Does a parellelogram have four congruent triangles?
Yes. Read on for why: Take a parallelogram ABCD with midpoints E and F in the bases. So something like this (forgive the "drawing"): A E B __.__ /__.__/ C F D We know that parallelogram AEFC = EBDF, since they have the same base (F bisects CD, so CF = FD), height (haven't touched that), and angles (<ACF = <EFD because they're parallel - trust me that everything else matches). We also know that every parallelogram can be divided into two congruent triangles along their diagonal. So if two congruent parallelograms consistent of two congruent triangles each, then all four triangles are congruent. So your congruent triangles are ACF, AEF, EFD, and EBD. You can further reinforce this through ASA triangle congruency proofs (as I did at first), but this is a far more concise and equally valid answer.
If you have 8 small triangles made of 16 lines how can you make four small triangles?
If you draw a single square, and then put one X through it, you have 4 triangles. Put another X through it and you have 8. Now, if you want to make four triangles, simply remove the two diagonal lines in the center, and it will create four triangles. Now, since they're separated by the other triangles, it would mean removing four lines, but that is still your answer.
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.
