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Notes – Lesson 6.4
Geometry
Name ________________________________
Rhombus:
Theorem 6.9:
Each diagonal of a rhombus _______________________ two angles of the rhombus.
Theorem 6.10: The diagonals of a rhombus are ______________________________.
Examples. Find the measures of the numbered angles in each rhombus.
1.
2.
3.
4.
<1 ______ <2 _______
<1 ________ <2 ________
<1 _________ <2 _________
<1 ________ <2 _________
<3 ______ <4 _______
<3 ________
<3 ________
<3 ________ <4 __________
5.
6.
7.
<1 ______ <2 _______
<1 ________ <2 ________
<1 _________ <2 _________
<3 ______ <4 _______
<3 ________
<3 ________
Rectangle:
Theorem 6.11:
 The diagonals of a rectangle are __________________________ and
_______________________________________________________.
Examples. LMNP is a rectangle. Find the value of x and the length of each diagonal.
1. LN = x and MP = 2x – 4
2. LN = 5x – 8 and MP = 2x + 1
3.
4.
AO = x + 2 and OC = 3x - 10
BO = 4x + 5 and OC = 2x + 12
Find x = __________
Find x = __________
AO = _________ AC = ________ BD = ________
BO = __________ BD = ________
5.
AC = __________
6.
<1 ________ <2 ________ <3 __________
<1 ________ <2 ________ <3 __________
Converse Theorems:

If one diagonal of a parallelogram bisects 2 angles of the parallelogram, then the parallelogram is a _________________

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a __________________.

If the diagonals of parallelogram are congruent, then the parallelogram is a ______________________.
Examples: Is the Parallelogram a Rhombus or a Rectangle?
1.
2.
3.
4.
5.
Finding the Area of a Rhombus
A rhombus is really 2 ________________________. Area for a triangle is: A = ____________ and multiply this answer by _____.
Examples – Find the area of each rhombus.
1)
2) BC = 10
AD = 8