Question

WXYZ is a parallelogram. Find each measure. $$x z$$

   WXYZ is a parallelogram. Find each measure.
$$x z$$

Geometry

Edward Burger, David… 1st Edition

Chapter 6, Problem 23

Instant Answer

Solved by Expert Ashley Volpe

05/21/2020

Step 1

Therefore, we can say that $XV = VZ$. Given that $XV = 3a - 7$ and $VZ = 2a$, we can set up the equation $3a - 7 = 2a$. Show more…

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WXYZ is a parallelogram. Find each measure. $$x z$$

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Key Concepts

Angle Relationships in Parallelograms

In any parallelogram, not only are the opposite angles congruent, but consecutive angles are supplementary, meaning they add up to 180°. This relationship is key for determining unknown angle measures within the figure.

Diagonal Properties

The diagonals of a parallelogram have the characteristic of bisecting each other, meaning that each diagonal cuts the other into two equal segments. This quality is often used in proofs and in solving problems involving segment lengths and congruence within the shape.

Parallelogram Properties

A parallelogram is a quadrilateral with two pairs of parallel sides. This definition implies that opposite sides are equal in length and opposite angles are equal in measure, which forms the foundation for solving various geometric problems related to shape congruence and angle measures.

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