1. 8.5 Rhombi and Squares What you’ll learn:
To recognize and apply the properties of rhombi.
To recognize and apply the properties of squares.

2. Rhombus
Rhombus – a quadrilateral with all 4 sides congruent. It has all the properties of a parallelogram. Theorem 8.15 – The diagonals of a rhombus are perpendicular. Theorem 8.16 – If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Theorem 8.17 – Each diagonal of a rhombus bisects a pair of opposite angles.

3. Rhombus Properties There are 8 properties of a rhombus:
Both pairs opposite sides parallel.
Both pairs of opposite angles congruent.
Both pairs of opposite sides congruent.
Consecutive angles are supplementary.
All 4 sides are congruent.
Diagonals bisect each other.
Diagonals are perpendicular
Diagonals bisect a pair of opposite angles.

4. Squares
Square – a quadrilateral that is both a rectangle and a rhombus. It has all the properties of both as well as those of the parallelogram.

5. Square Properties There are 10 properties of a square:
Both pairs opposite sides parallel.
Both pairs of opposite angles congruent.
Both pairs of opposite sides congruent.
Consecutive angles are supplementary.
All 4 sides are congruent.
All 4 angles are right.
Diagonals bisect each other.
Diagonals are perpendicular
Diagonals bisect a pair of opposite angles.
Diagonals are congruent.

6. Use rhombus LMNP and the given information to find each value.
Find y if m1=y²-54.
Find mPNL if
mMLP=64.
3. Find MQ if ML=5 and LQ=4. L M N P Q 1

7. Determine whether quadrilateral ABCD is a parallelogram, rhombus, a rectangle, or a square for A(-2,-1), B(-1,3), C(3,2), D(2,-2)
Find slope and distance of all 4 sides. Slope – will tell you if it is a parallelogram and also if it is a rectangle. (won’t tell you if it’s a rhombus or square) Distance – will tell you if it’s a rhombus. If it’s a rectangle and a rhombus, then it’s a square.

8. Homework p. 434 12-30 even, omit #24, 40, 48-58 even