Download Geometry Notes 10-5 Rhombus A rhombus is a parallelogram with

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Geometry
Notes 10-5
Rhombus
A rhombus is a parallelogram with two congruent consecutive sides.
A quadrilateral is a rhombus if any of the following can be proven true.
1. It is a parallelogram with two congruent consecutive sides.
2. It is equilateral
3. It is a parallelogram whose diagonals are perpendicular to each other.
4. It is a parallelogram whose diagonals bisect opposite angles.
Ex.1: PQRS is a rhombus and
. Prove that PR
divides the rhombus into two equilateral triangles.
P
S
60
Q R
Ex. 2 Given: ABCD is a parallelogram, with sides as represented in the
diagram.
B C
Prove: ABCD is a rhombus
2x + 1 3x ­ 11
A x + 13 D
1
Ex. 3 Given: rhombus MATH with MT=18 and
Find the perimeter of the rhombus.
A
M
T
H
Ex. 4 Quadrilateral WXYZ has coordinates W(1,10), X(-4,0), Y(7,2), and
Z(12,12).
a. Prove that WXYZ is a parallelogram.
b. Prove that WXYZ is a rhombus
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