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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.
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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 m1=y²-54. • Find mPNL if mMLP=64. 3. Find MQ if ML=5 and LQ=4. M 1 N L Q P
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.
