 1- Given a parallelogram MNPQ such that MN = 2a-3b and NO = 20-3b. Find the value of a and all possible value of b that make MNPQ a rhombus.   2- Given a quadrilateral ABCd such that ∠A... What is the area of a quadrilateral whose vertices are given?

What is the area in square units, of a quadrilateral whose vertices are (5,3), (6,-4), (-3,-2), (-4,7)? Prove that if a quadrilateral is a parallelogram then one pair of opposite angles are congruent

Given :  〉ABCD   Prove: ∠D ≅ ∠B   _D______________C |                  1      /...  Image 53k

Given that PQRS is a quadrilateral, prove that the sum of its interior angles is 360o. given ; PQRS is a quadrillateral. Prove;

GIVEN: PQRS is a quadrilateral        PROVE: measure of angle P + measure of angle PSR +measure of angle R+ measure of angle RQP = 360 Three points of a quadrilateral ABCD are A(1,2) B(6,7) C(9,6).

Three points of a quadrilateral ABCD are A(1,2) B(6,7) C(9,6). Given that AB=AD and BC=DC and F is the foot of perpendicular from B to line AC. Find coordinates of F and D. And area of quadrilateral... the coordinates of the quadrilateral VWXY are given below find the coordinates of its image after a dialation with the given scale factor which is 2.   v(6,2)  w(-2,4) x(-3,-2)... Properties of Trapezoids and Kites Now that we've seen several types of quadrilaterals that are parallelograms, let's learn about figures that do not have the properties of parallelograms. Recall that parallelograms were quadrilaterals whose opposite sides were parallel. In this section, we will look at quadrilaterals whose opposite sides may intersect at some point. The two types... read more Proving Quadrilaterals Are Parallelograms In the previous section, we learned about several properties that distinguish parallelograms from other quadrilaterals. Most of the work we did was computation-based because we were already given the fact that the figures were parallelograms. In this section, we will use our reasoning skills to put together two-column geometric proofs... read more Properties of Parallelograms The broadest term we've used to describe any kind of shape is "polygon." When we discussed quadrilaterals in the last section, we essentially just specified that they were polygons with four vertices and four sides. Still, we will get more specific in this section and discuss a special type of quadrilateral: the parallelogram. Before we... read more Polygons Before we get too caught up on the excitement of quadrilaterals, let's take time to learn the names and basic properties of different polygons. Polygons are two-dimensional, closed, plane shapes composed of a finite number of straight sides that meet at points called vertices. Triangles, which we have already learned about, are one type of polygon. In this section we will... read more Quadrilaterals Now that we've taken a detailed look at triangles, we can begin looking at a shape with an extra side and vertex: the quadrilateral. The word "quadrilateral" is composed of two main parts: (1) quad - which means "four", and (2) lateral - which means "side." While triangles are very significant to the world around us, quadrilaterals... read more Areas of Trapezoids Recall that a trapezoid is a quadrilateral defined by one pair of opposite sides that run parallel to each other. These sides are called bases, whereas the opposite sides that intersect (if extended) are called legs. Let's learn how to measure the areas these figures. Determining the area of a trapezoid is reliant on two main components of these polygons:... read more Areas of Rhombuses and Kites Although a rhombus is a type of parallelogram, whereas a kite is not, they are similar in that their sides have important properties. Recall that all four sides of a rhombus are congruent. Kites, on the other hand, have exactly two pairs of consecutive sides that are congruent. This characteristic of kites does not allow for both pairs of opposite sides... read more Prove: if a quadrilateral has one pair of sides both parallel and congruent then the quadrilateral is a parallelogram.

I think I have to prove that the other opposite sides are also parallel, but I am not sure how to do it. It is given that the other opposite sides are congruent and parallel. ABCD is a rectangle in which diagonals AC bisects angle A as well as angle C. Show that ABCD is a squre.