Algeo 3 {Mr. Yealu}
Thurs., 12-06-2012 Name: _____________________
6.4: Rhombuses, Rectangles, and Squares
A rhombus is a parallelogram with four congruent sides.
A rhombus is an equilateral parallelogram.
The diagonals of a rhombus are perpendicular and angle bisectors.
All the properties of a parallelogram apply by definition.
All the properties of a kite apply.
The diagonals are perpendicular bisectors of each other.
The diagonals divide the rhombus into four congruent right triangles.
A rectangle is a parallelogram with four right angles.
A rectangle is an equiangular parallelogram.
The diagonals of a rectangle are congruent.
All the properties of a parallelogram apply by definition.
A square is a parallelogram with four congruent sides and four right angles.
A square is both a rectangle and a rhombus.
A square is an equilateral rectangle or an equiangular rhombus.
A square is a regular (both equilateral and equiangular) parallelogram.
The diagonals of a square are congruent, perpendicular, and angle bisectors.
All the properties of a parallelogram apply by definition.
All the properties of a rectangle apply by definition.
All the properties of a rhombus apply by definition.
The diagonals form four isosceles right triangles. 45-45-90 triangles
6.5: Trapezoids
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are
the bases. The nonparallel sides are the legs.
Please note very well: A trapezoid is never a parallelogram; and a parallelogram is never a trapezoid.
A trapezoid has two pairs of base angles.
If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.
The lower base angles of an isosceles trapezoid are congruent.
The upper base angles of an isosceles trapezoid are congruent.
The diagonals of an isosceles trapezoid are congruent.
Any lower base angle of an isosceles trapezoid is supplementary to any upper base angle.
Kites
A kite is a quadrilateral in which two disjoint pairs of consecutive sides are congruent.
The diagonals of a kite are perpendicular. Please note very well: A kite may be a parallelogram.
One diagonal {the longer one} is the perpendicular bisector of the other {the shorter one}.
One of the diagonals {the longer diagonal} bisects a pair of opposite angles.
One pair of opposite angles {the opposite angles at the ends of the shorter diagonal} are congruent.
Always (A), Sometimes (S), or Never (N):
1. A rhombus is a parallelogram.
1. ____
2. A parallelogram is a rhombus.
2. ____
3. A rectangle is a parallelogram.
3. ____
4. A parallelogram is a rectangle.
4. ____
5. A rectangle is a square.
5. ____
6. A square is a rectangle.
6. ____
7. A rectangle is equiangular.
6.5 homework: pp. 334 – 336 #’s 1 – 25, 34 - 35
7. ____
8. A rectangle is equilateral.
8. ____
9. A rhombus is equilateral.
9. ____
10. A rhombus is equiangular.
10. ____
11. A rhombus is a rectangle.
11. ____
12. A rectangle is a rhombus.
12. ____
13. A rhombus is a quadrilateral.
13. ____
14. A square is a parallelogram.
14. ____
Theorem 6.12: If a trapezoid is isosceles, then each pair of base angles is congruent.
Theorem 6.13: If a trapezoid has a pair of congruent base angles, then it is isosceles.
Definition: A right trapezoid is a trapezoid that contains a right angle.
Can a trapezoid contain exactly one right angle?

Can a trapezoid contain more than two right angles?
The midsegment (or median) of a trapezoid is the segment that connects the midpoints of
its legs.
(1) The midsegment (or median) of a trapezoid is parallel to the bases.
(2) The length of the midsegment (or median) is half the sum of the lengths of the bases.