Chapter 5: Q3 (page 195)

Quadrilateral WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
$\bar{W X} ≅ \bar{Y Z}, \bar{X Y} ≅ \bar{Z W}$ and $diag. \bar{W Y} ≅ diag. \bar{X Z}$

Short Answer

Expert verified

The quadrilateral is a rectangle.

Step by step solution

Step 1. Apply the following concept.

If both pairs of opposite sides of a quadrilateral are equal, then it's a parallelogram.

The diagonals of a rectangle are congruent.

Step 2. Step description.

Consider that $\bar{W X} ≅ \bar{Y Z}, \bar{W X} | | \bar{Y Z}$ .

That is, both pairs of opposite sides of the quadrilateral are congruent.

Since one pair of the quadrilateral is parallel and congruent, therefore the quadrilateral is a parallelogram.

Step 3. Step description.

Also $diag. \bar{W Y} ≅ diag. \bar{X Z}$ .

Since the diagonals are congruent, thus the parallelogram is a rectangle.

Therefore, the parallelogram is a rectangle.

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Quadrilateral WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
$\bar{W X} ≅ \bar{Y Z}, \bar{X Y} ≅ \bar{Z W}$ and $diag. \bar{W Y} ≅ diag. \bar{X Z}$

Short Answer

Step by step solution

Step 1. Apply the following concept.

Step 2. Step description.

Step 3. Step description.

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Quadrilateral WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.WX¯≅YZ¯,XY¯≅ZW¯anddiag.WY¯≅diag.XZ¯

Short Answer

Step by step solution

Step 1. Apply the following concept.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Calculus

Probability and Statistics

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Geometry

Study anywhere. Anytime. Across all devices.

Quadrilateral WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.
$\bar{W X} ≅ \bar{Y Z}, \bar{X Y} ≅ \bar{Z W}$ and $diag. \bar{W Y} ≅ diag. \bar{X Z}$