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RHOMBUS
GEOMETRY
DATE __________ Per.___________
Quadrilaterals
questions a-w below.
1. Answer
Then in parts x,y, and z,
complete each theorem.
H
NAME_________________________
R
1 2
8
7
B
3
4
M
6 5
O
a) A rhombus is an equilateral quadrilateral. State which four sides are congruent.
b) According to the reflexive property, RO = ?
c) Why is HM = MH?
d) What triangle congruence conditions justifies ∆HRM ≅ ∆ MOH?
e) What other two triangles are congruent by Side-Side-Side?
f) Why is ∠4≅∠8?
g) What other two angles are congruent by CPCTC?
h) Name two other pairs of congruent angles.
i) Since ∆MRH and ∆HOM have two congruent sides, they are what kind of triangles?
j) Why is ∠8 ≅ ∠3?
k) What angle is congruent to ∠7?
l) Name two other pairs of congruent angles according to the Isosceles Triangle Theorem.
m) Since ∠1 ≅ ∠5, what lines are parallel by the Converse of the A.I.A. Thm.?
n) What pair of alternate interior angles are needed to claim that RM // HO?
o) Name all angles congruent to ∠1:
p) Name all other congruent angles.
q) Since ∠5 ≅ ∠6, what does OB do to ∠HOM?
r) Name the bisectors of the remaining interior angles of the rhombus.
s) The Isosceles ∆ Vertex Corollaries justify the conclusion that RO is what kind of bisector?
t) What kind of angle is ∠RBH? Why?
u) Name all angles congruent to ∠RBH:
v) How are the segments HM and RO related?
w) Are ∆RBH, ∆HBO, ∆MBO, and ∆MBR congruent? Why?
x) THEOREM: The diagonals of a rhombus are:
y) THEOREM: What bisects the opposite angles of a rhombus?
z) THEOREM: A rhombus is also a: