Chapter 4.3, Problem 31E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Are quadrilaterals ABCD and EFGH congruenta) if both are squares and A B ¯ ≅ E F ¯ ? b) if each is a rhombus and A B ¯ ≅ E F ¯ ?

To determine

(a)

To find:

AB¯EF¯, if both are squares.

Explanation

The quadrilateral if all the sides are equal it is called square or rhombus.

The properties of square:

1) All the properties of a rhombus apply (the ones that matter here are parallel sides, diagonals are perpendicular bisects of each other, and diagonals bisect the angles).

2) All the properties of a rectangle apply (the only one that matters here is diagonals are congruent).

3) All sides are congruent.

4) All angles are right angles.

Calculation:

Given:

Let us take both ABCD and EFGH are squares.

Step 1:

Now we have to find both squares are congruent or not.

All squares are not congruent. But all squares are similar.

Two polygons are similar if the angles of one polygon have an exact match in the other polygon, and the ratio of corresponding side lengths between the two polygons is constant.

This is true of all squares, since all squares have four 90-degree angles, and the ratio of the length of a side of the two squares is identical.

So, both the squares ABCD and EFGH are congruent...

To determine

(b)

To find:

AB¯EF¯, if both are rhombus.

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