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How do you prove that the diagonals of a square are perpendicular to each other?
Wiki User
∙ 13y ago
You can use slope to measure the diagonals. If the product of their slopes is -1 then they are perpendicular.
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Draw a square. Note the coordinates for the corners. For instance, my corners are (0,0), (1,0), (1,1), and (0,1). Consider each diagonal (0,0)-(1,1) and (1,0)-(0,1)
Recall that the slope of a line is delta y over delta x. The slope of the first diagonal is 1, while the slope of the second diagonal is -1. 1 times -1 is -1, which means that the diagonals are perpendicular.
Note: This works for any square, except where one of the diagonals has infinite slope, i.e. a vertical line. In that case, you can simply state that one diagonal has infinite slope and the other diagonal has zero slope. The math does not work, because this proof is based on Cartesian coordinates. You can make it work by converting to polar coordinates and comparing the two thetas. They should have a relationship where the absolute value of theta 1 minus theta 2 is equal to pi.
Wiki User
∙ 13y ago
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What are the proofs that a quadrilateral ia s parallelogram?
There are 5 ways to prove a Quadrilateral is a Parallelogram. -Prove both pairs of opposite sides congruent -Prove both pairs of opposite sides parallel -Prove one pair of opposite sides both congruent and parallel -Prove both pairs of opposite angles are congruent -Prove that the diagonals bisect each other
How can you prove that a constructed line is parallel to a given line Assume that the transversal line is not perpendicular to the other lines.?
By using a protractor which will show that corresponding angles are equal and alternate angles are equal .
How can you prove that a constructed line is parallel to a given line if the transversal in not perpendicular?
Show that corresponding angles are congruent?
How can you prove that a triangle is 180 degrees?
its half a square and a square is 360
State and prove the parallel axis theorem?
the moment of inertia of a body about a given axis is equal to the sum of its moment of inertia about a parallel axis passing through its centre of mass and the product of its mass and square of perpendicular distance between two axis Iz=Ix+Iy
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.
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.
Prove that the diagonals of rectangle are equal?
prove any two adjacent triangles as congruent
How do you prove that the diagonals of a square are equal and bisect each other at right angles?
it would produce two right angle triangleImproved Answer:-Measure them and use a protractor which will result in equal measures of 4 by 90 degrees angles
Prove that a rhombus has congruent diagonals?
Since the diagonals of a rhombus are perpendicular between them, then in one forth part of the rhombus they form a right triangle where hypotenuse is the side of the rhombus, the base and the height are one half part of its diagonals. Let's take a look at this right triangle.The base and the height lengths could be congruent if and only if the angles opposite to them have a measure of 45⁰, which is impossible to a rhombus because these angles have different measures as they are one half of the two adjacent angles of the rhombus (the diagonals of a rhombus bisect the vertex angles from where they are drawn), which also have different measures (their sum is 180⁰ ).Therefore, the diagonals of a rhombus are not congruent as their one half are not (the diagonals of a rhombus bisect each other).
How do you prove the diagonals of an isosceles triangle congruent?
You can't because triangles do not have diagonals but an isosceles triangle has 2 equal sides
Show that if diagonals of a quadrilateral bisects each other then it is a rhombus?
This cannot be proven, because it is not generally true. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. And conversely, the diagonals of any parallelogram bisect each other. However not every parallelogram is a rhombus.However, if the diagonals are perpendicular bisectors, then we have a rhombus.Consider quadrilateral ABCD, with diagonals intersecting at X, whereAC and BD are perpendicular;AX=XC;BX=XD.Then angles AXB, BXC, CXD, DXA are all right angles and are congruent.By the ASA theorem, triangles AXB, BXC, CXD and DXA are all congruent.This means that AB=BC=CD=DA.Since the sides of the quadrilateral ABCD are congruent, it is a rhombus.
How do you prove the diagonal lines in a parallelogram is not a rhombus?
Because the diagonals of a rhombus intersect each other at 90 degrees whereas in a parallelogram they don't
What are necessary when proving that the diagonals of a rectangle are congruent?
A ruler or a compass would help or aternatively use Pythagoras' theorem to prove that the diagonals are of equal lengths
What is the difference between a rhombus and a square?
The difference is a rhombus is made up of 2 acute and 2 obtuse angles and a square is made up of 4 right angles. On a square, both of the diagonals equal each other, but on a rhombus the diagonals can equal each other, but it's possible for them to not equal each other.
How do you prove that a shape is a rectangle?
Check to see that -- it has four sides -- its two diagonals are equal.
What are the proofs that a quadrilateral ia s parallelogram?
There are 5 ways to prove a Quadrilateral is a Parallelogram. -Prove both pairs of opposite sides congruent -Prove both pairs of opposite sides parallel -Prove one pair of opposite sides both congruent and parallel -Prove both pairs of opposite angles are congruent -Prove that the diagonals bisect each other
