Download Bell Ringer 5.5: 1. Given the quadrilateral is a rhombus find the

Bell Ringer 5.5:
1. Given the quadrilateral is a rhombus find the following:
a. If m<BCD = 64, find m<BAC.
b. If AB = 2x + 3 and BC = x + 7, find CD.
Homework due Wednesday:
6.5: Pg. 435 ­ 438 (8 ­ 64, every 4th)
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Today's objectives:
­ Recognize and apply the properties of rhombi and squares.
­ Determine whether quadrilaterals are rectangles, squares, or rhombi.
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Vocabulary Terms:
Rhombus ­ A parallelogram with all four sides equal
Square ­ A parallelogram with four congruent sides and four right angles Rhombus ­ diagonals are perpendicular
­ Each diagonal bisects a pair of opposite angles
If a quadrilateral is both a rectangle and a rhombus then it is a square.
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Properties of a Rhombus:
a. m<FJH = 82, find m<KHJ
b. If GH = x + 9 and JH = 5x ­2, find x.
c. IF FK = 5 and FG = 13, find KJ
d. If m<JFK = 6y + 7 and m<KFG = 9y ­ 5, find y.
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Proofs for Rhombi and Squares:
a. Given: JKLM is a parallelogram
Triangle JKL is isosceles
Prove: JKLM is a rhombus
b. Given: SQ is a perpendicular bisector of PR
PR is a perpendicular bisector of SQ
Triangle RMS is isosceles
Prove: PQRS is a square
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What is my shape?
a. Parallelogram JKLM has vertices J(­7,­2), K(0, 4), L (9, 2) and M(2, ­4). Is it a rectangle, rhombus, or a square? (list all that apply)
b. Parallelogram JKLM has vertices J(5, 0), K(8, ­11), L(­3, ­14) and M(­6, ­3). Is it a rectangle, rhombus, or a square? (list all that apply)
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