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Prove that if the diagonal of a parallelogram does not bisect the angles through the vertices to which the diagonal is drawn the parallelogram is not a rhombus?
Suppose that the parallelogram is a rhombus (a parallelogram with equal sides). If we draw the diagonals, isosceles triangles are formed (where the median is also an angle bisector and perpendicular to the base). Since the diagonals of a parallelogram bisect each other, and the diagonals don't bisect the vertex angles where they are drawn, then the parallelogram is not a rhombus.
How many triangles are formed by the diagonals from six vertices of a hexagon?
The three major diagonals in an ordinary hexagon do not intersect at the same point. Therefore, in such a hexagon, the diagonals form 111 triangles.
Which point in a triangle is equidistant from the vertices's of the triangle?
Not sure about vertices's. The circumcentre is equidistant from a triangle's vertices (no apostrophe).
Does a rhombus have at least have one right angle?
The vertices of a rhombus have no right angles but its diagonals intersect each other at right angles.
What shapes have diagonals bisect vertex angles?
Only a square and a rhombus will have all its diagonals bisecting vertices. In other shapes some - but not all - diagonals can bisect vertices.
Do the point at which the diagonals of a parallelogram intersect is always equidistant from the four vertices?
No because the diagonals of a parallelogram are of different lengths
The point at which the diagonal of a parallelogram intersect is equidistant from the four vertices?
sometimes
The point at which the diagonals of a parallelogram intersect is. equdistant from the four vertices?
The statement is no true.
How do you construct a parallelogram whose one side and two diagonals are given?
To construct a parallelogram with one side and two diagonals given, start by drawing the given side as one of the sides of the parallelogram. Label the endpoints of this side. Then, using a compass, draw arcs from each endpoint of the side with radii equal to the lengths of the diagonals, intersecting at two points. These intersection points will be the other two vertices of the parallelogram. Finally, connect these vertices to form the complete parallelogram.
Prove that if the diagonal of a parallelogram does not bisect the angles through the vertices to which the diagonal is drawn the parallelogram is not a rhombus?
Suppose that the parallelogram is a rhombus (a parallelogram with equal sides). If we draw the diagonals, isosceles triangles are formed (where the median is also an angle bisector and perpendicular to the base). Since the diagonals of a parallelogram bisect each other, and the diagonals don't bisect the vertex angles where they are drawn, then the parallelogram is not a rhombus.
How many triangles are formed by the diagonals from six vertices of a hexagon?
The three major diagonals in an ordinary hexagon do not intersect at the same point. Therefore, in such a hexagon, the diagonals form 111 triangles.
What are the lengths of the diagonals and their point of intersection of a quadrilateral with vertices at 1 7 and 7 5 and 6 2 and 0 4?
The given vertices when plotted on the Cartesian plane forms a rectangle with diagonals of square root of 50 in lengths and they both intersect at (3.5, 4.5)
Do the diagonals of a kite intersect at 90 degree angles?
Yes, the diagonals of a kite intersect at right angles (90 degrees). In a kite, one diagonal connects the vertices of the two pairs of equal-length sides, while the other diagonal connects the vertices of the unequal angles. This unique property of kites ensures that the diagonals are perpendicular to each other.
Which point in a triangle is equidistant from the vertices's of the triangle?
Not sure about vertices's. The circumcentre is equidistant from a triangle's vertices (no apostrophe).
Is the centroid equidistant from the vertices's of a triangle?
No. and it is not vertices's! vertices will do.
Does a rhombus have at least have one right angle?
The vertices of a rhombus have no right angles but its diagonals intersect each other at right angles.
Which term describes the point where the perpendicular bisectors of the sides of a triangle intersect?
The point where the perpendicular bisectors of the sides of a triangle intersect is called the circumcenter. This point is equidistant from all three vertices of the triangle and serves as the center of the circumcircle, which is the circle that passes through all the vertices of the triangle.
