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The x and y axis need to be perpendicular to each other in order for them to intersect each other at the point of origin (0, 0) on the Cartesian plane,
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Must a bisector of a segment always be a perpendicular line?
Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.
In a parallelogram the diagonals are perpendicular bisectors of each other What kind of parallelogram must the figure be?
It is a rhombus
Is it true that The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
no
How do you construct a perpendicular bisector of each side of a parallelogram?
With a compass and a straight edge and the lines must bisect each other at 90 degrees
Can perpendicular lines be parallel lines?
It is impossible for parallel lines to be perpendicular. Perpendicular lines are intersecting lines, meaning that they cross each other. Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended in either direction. So intersecting lines (which includes perpendicular lines) and parallel lines are exact opposites. Parallel lines will never meet or cross; they cannot be perpendicular.
Must a bisector of a segment always be a perpendicular line?
Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.
The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False
The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram.?
false
In a parallelogram the diagonals are perpendicular bisectors of each other What kind of parallelogram must the figure be?
It is a rhombus
Is it true that The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
no
What must be true about the slopes of 2 perpendicular lines?
The slopes of two perpendicular lines are negative inverses of each other. In other words, the two slopes when multiplied together equal -1.
How do you construct a perpendicular bisector of each side of a parallelogram?
With a compass and a straight edge and the lines must bisect each other at 90 degrees
State and prove perpendicular axis and parallel axis theorem?
In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:
Can perpendicular lines be parallel lines?
It is impossible for parallel lines to be perpendicular. Perpendicular lines are intersecting lines, meaning that they cross each other. Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended in either direction. So intersecting lines (which includes perpendicular lines) and parallel lines are exact opposites. Parallel lines will never meet or cross; they cannot be perpendicular.
Why are the diagonals of a square perpendicular bisectors of each other?
You could prove this by congruent triangles, but here are two simpler arguments: --------------- Since a square is a rhombus, and the diagonals of a rhombus are perpendicular bisectors of each other, then the diagonals of a square must be perpendicular bisectors of each other -------------------- A square has four-fold rotational symmetry - as you rotate it around the point where the diagonals cross, there are four positions in which it looks the same. This means that the four angles at the centre must be equal. They will each measure 360/4 = 90 degrees, so the diagonals are perpendicular. Also. the four segments joining the centre to a vertex are all equal, so the diagonals bisect each other.
State ane prove perpendicular axis theorem?
In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:DerivationWorking in Cartesian co-ordinates, the moment of inertia of the planar body about the axis is given by[2]: On the plane, , so these two terms are the moments of inertia about the and axes respectively, giving the perpendicular axis theorem.
True or false the diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.
