Question

In: Math

Perpbisogram Definition: A perpbisogram of a quadrilateral is a polygon formed by the perpendicular bisectors of...

Perpbisogram Definition: A perpbisogram of a quadrilateral is a polygon formed by the perpendicular bisectors of the sides of the quadrilateral.

Prove the following theorem

  1. The angles of a trapezoid are congruent to the angles of its perpbisogram.

(SHOW DIAGRAM)

Solutions

Expert Solution


Related Solutions

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.
In a quadrilateral ABCD, the angle bisectors are constructed. Prove that the angle bisectors enclose a...
In a quadrilateral ABCD, the angle bisectors are constructed. Prove that the angle bisectors enclose a cyclic quadrilateral.
a picture of these three. (a) Circumcentre : Draw perpendicular bisectors of the three sides. The...
a picture of these three. (a) Circumcentre : Draw perpendicular bisectors of the three sides. The point where they meet is the Circumcentre. (b) Orthocentre : Draw the perpendiculars from the third vertex for each of the three sides. The point where they meet is the Orthocentre. (c) Incentre : Draw angle bisectors for each of the three angles. The point where they meet is the Incentre.
Why do  perpendicular bisectors of the three sides of a triangle all meet at a single point?...
Why do  perpendicular bisectors of the three sides of a triangle all meet at a single point? and also why do  angle bisectors of the three sides of a triangle all meet at a single point ?
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.
Match the words with the correct definition. Perpendicular Parallel Colinear Fix Horizontal Definitions Defines a location...
Match the words with the correct definition. Perpendicular Parallel Colinear Fix Horizontal Definitions Defines a location and size for an entity. Aligns two entities. Defines two entities as 90 degree apart. Defines a line in the X direction. Defines an entity equidistant from another entity.
A convex polygon is defined as a polygon where all its internalangles are less than...
A convex polygon is defined as a polygon where all its internal angles are less than 180 degrees and no edges cross each other. You can assume the vertex with the smallest x-coordinate (assuming origin at bottom left) is the first coordinate and other vertices are numbered in a counter-clockwise direction. Figure 1 shows an example of such a polygon where V[1] is the first polygon. For simplicity, you can also assume all polygon vertices have distinct x and y...
every quadrilateral tessellates the plane. However, can an arbitrary quadrilateral such as the one shown below...
every quadrilateral tessellates the plane. However, can an arbitrary quadrilateral such as the one shown below have all its sides altered and still tessellate the plane? Decide which methods described in this activity set you can use to alter the sides of this quadrilateral and tessellate the plane. In the pictured quadrilateral, no sides are of equal length and no sides are parallel. For each method you use, make a template for your figure, and determine whether or not it...
Complete exercise 9.20 from the text. (a) Create a function called polygon that draws a polygon...
Complete exercise 9.20 from the text. (a) Create a function called polygon that draws a polygon in a polar plot. Your function should have a single input parameter – the number of sides. (b) Use a for loop to create a figure with four subplots…You should use the function you created in part (a) to draw each polygon. Use the index parameter from the for loop to specify the subplot in which each polygon is drawn, and in an expression...
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT