Geometry / Unit 7: Polygons and Quadrilaterals
7.4 Rectangles, Rhombuses and Squares
Notes
These are special parallelograms, so they have every parallelogram property, plus more.
- Rectangle: four right angles. Its diagonals are congruent.
- Rhombus: four congruent sides. Its diagonals are perpendicular and bisect the angles.
- Square: both a rectangle and a rhombus, so it has all of these properties.
- Example: rectangle $ABCD$ with $AC = 3x + 2$ and $BD = 5x - 6$ gives $3x + 2 = 5x - 6$, so $x = 4$.
Practice
Which quadrilateral always has perpendicular diagonals?
Rhombus diagonals are perpendicular.
In rectangle $JKLM$, $JL = 26$. What is $KM$?
Diagonals of a rectangle are congruent.
In rhombus $ABCD$, $m\angle BAC = 32^\circ$, where $\overline{AC}$ is a diagonal. Find $m\angle BAD$.
A rhombus diagonal bisects the angle, so $m\angle BAD = 2 \cdot 32 = 64^\circ$.
Ready for more? Take the Unit 7 test.