Chapter 11.4, Problem 29HP

To determine

To describe: The characteristics, that a square share with a rectangle and with a rhombus.

Answer to Problem 29HP

Square shares following characteristics with rectangle and rhombus:

1. Similarity of square with rectangle: (i) Both are parallelograms.

(ii) Each angle of both is 90 degree.

(iii) Diagonals of both are equal and bisect each other.

(iv) Diagonals of both bisect the opposite angles.

(v) Opposite sides are always equal in both.

2. Similarity of square with rhombus: (i) Both are parallelograms.

(ii) All four sides of both are equal to each other.

(iii) Diagonals of both are equal and bisect each other.

(iv) Diagonals of both bisect the opposite angles.

(v) Opposite sides are always equal in both.

(vi) Diagonals bisect each other at 90 degree.

Explanation of Solution

Given information: A square, a rhombus and a rectangle.

Concept used: Square, rhombus and rectangles all three are parallelograms. In square all sides are equal and each angle is of 90 degree and its diagonals are equal, bisecting each other. In rectangle, only opposite sides are equal and each angle is also of 90 degree and its diagonals also bisect each other and are equal. In rhombus, all sides are equal but no angle is of 90 degree and also diagonals are not equal, even bisecting each other always.

Conclusion: Based on above concept, the similarity between square and rectangle and square and rhombus can easily be characterized as shown in “answer” section.