Prove that if two of the opposite sides of a quadrilateral are respectively the greatest and...

Prove that if two of the opposite sides of a quadrilateral are respectively the greatest and the least sides of the quadrilateral, then the angles adjacent to the least are greater than their opposite angles

Expert Solution

milcah answered 1 year ago

Prove that if two of the opposite sides of a quadrilateral are respectively the greatest and...

Prove that if two of the opposite sides of a quadrilateral are respectively the greatest and the least sides of the quadrilateral, then the angles adjacent to the least are greater than their opposite angles.

Prove that the quadrilateral enclosed by the perpendicular bisectors of the sides of a rhombus is...

Prove that the quadrilateral enclosed by the perpendicular bisectors of the sides of a rhombus is a rhombus.

Show that if the opposite angles of a quadrilateral add up to two right angles, then...

Show that if the opposite angles of a quadrilateral add up to two right angles, then the vertices are concyclic

All of the sides of a quadrilateral are congruent if it is a rhombus.

The following conditional statement is true.All of the sides of a quadrilateral are congruent if it is a rhombus.Which of the following statements must also be true?a) If not all of the sides of a quadrilateral are congruent, then it is not a rhombus.b) If a quadrilateral is not a rhombus, then all of its sides are not congruent.c) If a quadrilateral is a rhombus, then not all of its sides are congruent.d) If all of the sides of a...

Prove the following theorem: In a Pasch geometry, a quadrilateral is a convex quadrilateral if and...

Prove the following theorem: In a Pasch geometry, a quadrilateral is a convex quadrilateral if and only if the vertex of each angle is contained in the interior of the opposite angle.

Problem #5 : a) Two positive charges, Qa and Qb are placed on opposite sides of...

Problem #5 : a) Two positive charges, Qa and Qb are placed on opposite sides of a grounded sphere of radius R at distances of 3R and 6R, respectively, from the sphere center. Show that Qb is repelled from the sphere if Qb < QA * (72275/87723) b) A infinite wire with line charge density λ is placed a distance d above a grounded conducting plane. Assume that the wire is parallel to the x-axis and is located at in...

Prove the following using the triangle inequality: Given a convex quadrilateral, prove that the point determined...

Prove the following using the triangle inequality: Given a convex quadrilateral, prove that the point determined by the intersection of the diagonals is the minimum distance point for the quadrilateral - that is, the point from which the sum of the distances of the vertices is minimal.

Draw ? on a torus (or the schematic representation where opposite sides of a rectangle are...

Draw ? on a torus (or the schematic representation where opposite sides of a rectangle are identified.)

Prove: A quadrilateral is a square if and only if its diagonals are congruent and bisect...

Prove: A quadrilateral is a square if and only if its diagonals are congruent and bisect each other at right angles.

In Euclidean geometry, a rhombus is a simple quadrilateral whose four sides all have the same...

In Euclidean geometry, a rhombus is a simple quadrilateral whose four sides all have the same length. If lengths of each of the sides are a and the distance between the parallel sides (known as height) is h, then the area of the rhombus is defined as a × h. Suppose that you already have a class named Rhombus that can hold a and h. The class has a method to compute the area as well. The class is as...

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Prove that if two of the opposite sides of a quadrilateral are respectively the greatest and...

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Prove that if two of the opposite sides of a quadrilateral are respectively the greatest and...

Prove that the quadrilateral enclosed by the perpendicular bisectors of the sides of a rhombus is...

Show that if the opposite angles of a quadrilateral add up to two right angles, then...

All of the sides of a quadrilateral are congruent if it is a rhombus.

Prove the following theorem: In a Pasch geometry, a quadrilateral is a convex quadrilateral if and...

Problem #5 : a) Two positive charges, Qa and Qb are placed on opposite sides of...

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