Section 6.4 –Rhombuses, Rectangles, and Squares
*Watch this video to give you a better grasp of the concepts listed below.*
-Rhombus:
- Rectangle:
- Square:
Example 1: Decide whether the statement is always, sometimes or never true.
a. A rectangle is a square.
b. A square is a rhombus.
c. A rhombus is a rectangle.
d. A rhombus is a square.
e. A rectangle is a rhombus.
f. A square is a rectangle.
g. A rectangle is a parallelogram.
Corollaries about Special Quadrilaterals
Rhombus Corollary:
A quadrilateral is a rhombus if and only if it has four congruent sides.
Rectangle Corollary:
A quadrilateral is a rectangle if and only if it has four right angles.
Square Corollary:
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
Example 2: Find the side lengths of this rhombus.
Theorem 6.11:
Theorem 6.12:
Theorem 6.13:
Example 3: Find the following given
a)
b) BC
Example 4:
Given that PQRS is a parallelogram, decide whether it is a rectangle, rhombus, square or none of these.
Justify your answer with work and explanation.