8.5 Rhombi and Squares What you’ll learn:

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Presentation transcript:

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.

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.

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.

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.

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.

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

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.

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