Bell Ringer. Rhombi Rectangles & Squares. Rhombus. Definition:. A rhombus is a parallelogram with four congruent sides. Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. ≡. ≡.
Lesson 6-4: Rhombus & Square
A rhombus is a parallelogram with four congruent sides.
Since a rhombus is a parallelogram the following are true:
The diagonals of a rhombus are perpendicular.
Each diagonal of a rhombus bisects a pair of opposite angles.
Given: ABCD is a rhombus. Complete the following.
A square is a parallelogram with four congruent angles and four congruent sides.
Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals.
Given: ABCD is a square. Complete the following.
A rectangle is a parallelogram with four right angles.
A rectangle is a special type of parallelogram.
Thus a rectangle has all the properties of a parallelogram.
CProperties of Rectangles
If a parallelogram is a rectangle, then its diagonals are congruent.
Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles.
If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.
x = 9 units
x = 18 units