rhombus

1. WELCOME TO MATH
CLASS
Ms. Sarah Jane D. Nomo

6. properties of a rhombus

7. Learning objectives
• define rhombus;
• state the different properties of rhombus;
• apply the theorems of rhombus in solving
problems; and
• appreciate the importance of rhombus in
real-life.

8. Am i a rhombus
or not?

11. Rhombus
Not
Rhombus
or

12. or
Rhombus
Not
Rhombus

13. Not Rhombus
Rhombus
or

14. Rhombus
Not Rhombus
or

15. Rhombus
Not Rhombus
or

16. Rhombus
Not Rhombus
or

17. Not Rhombus
Rhombus
or

18. or
Not Rhombus
Rhombus

19. Rhombus
Not Rhombus

20. Rhombus
Not Rhombus

22. "RHOMBUS

23. It is defined as a parallelogram
with four congruent sides. Just
like the rectangle, it has the
properties of a parallelogram. The
rhombus has special properties as
well.

24. 7 properties of rhombus

25. All four sides are congruent
FA≅AD
AD≅DE
DE≅EF
EF≅FA
—
— —
—
—
—
— —

26. All four sides are congruent
FA= 8cm
AD= 8cm
DE= 8cm
EF= 8cm
—
—
FA≅AD
AD≅DE
DE≅EF
EF≅FA
—
— —
—
—
—
— —
—
—

27. Opposite sides are parallel
>
FA || ED
EF || DA
—
—
— —

28. Opposite angles are congruent .
>
∠F≅∠D
∠E≅∠A

29. Opposite angles are congruent .
>
If the m∠F =120° , what is
the m∠D?

30. Opposite angles are congruent .
>
If the m∠F =120° , what is
the m∠D?
Answer: 120°

31. Opposite angles are congruent .
>
If the m∠E =60°, what is
the m∠A?

32. Opposite angles are congruent .
>
If the m∠E =60°, what is
the m∠A?
Answer: 60°

33. Adjacent angles are supplementary.
>
120°
120°
60°
60°
IF:
∠F+∠A=180°
∠A+∠D=180°
∠D+∠E=180°
∠E+∠F=180°

34. Adjacent angles are supplementary.
THEN:
∠F+∠A=120°+60°=180°
∠A+∠D=60°+120°=180°
∠D+∠E=120°+60°=180°
∠E+∠F=60°+120°=180°
>
120°
120°
60°
60°

35. Diagonals bisect each other and are
perpendicular
>
.
FD and AE are diagonals, and
they intersects at Point S
m∠FSA=90°
m∠ASD=90°
m∠DSE=90°
m∠ESF=90°
— —
.
.
.
.

36. Diagonals bisect each other and are
perpendicular
.
4
FADE is a rhombus with
diagonals intersecting at S.
FS + DS = 4 + 4 = 8
The total measurement of FD is
8
—
—
—

37. Diagonals bisect each other and are
perpendicular
.
4
1
2
FADE is a rhombus with
diagonals intersecting at S.
The measurement of AE = 12
AS + ES = 6 + 6 =
12
—
— —

38. Each diagonal bisects a pair of opposite angles.
>
□FADE is a rhombus if and
only FD bisects angle ∠ADE
and ∠AFE
and AE bisects ∠FAD and ∠FED.
—
—

39. Each diagonal separates the rhombus into two
congruent triangles.
>
FD is
diagonal
∆FED≅∆DAF
∆DEF≅∆FAD
—

40. Find the measures of sides if KI=12x and
DN=2(4x+6)
Solve for x:
12x=2(4x+6)
12x=8x+12
12x
2(4x+6)
—
—
.
12x-8x=12
4x=12
4x = 12
_ _
4 4 x=3

41. Find the measures of sides if KI=12x and
DN=2(4x+6)
KI=12x
=12(3)
=36
12x
2(4x+6)
—
—
.
Therefore, all four
sides have a
measurement of 36

42. .
□RICE: Find the measurement of the following if m∠RIC=100
R
I
C
E
a.) m∠REC
b.) m∠ICE
c.) m∠ICR
d.) m∠IEC

43. □RICE: Find the measurement of the following if m∠RIC=100°
R
C
.
I
E
a.) m∠REC
m∠REC = m∠RIC
m∠REC = 100°

44. □RICE: Find the measurement of the following if m∠RIC=100°
R
C
m∠ICE+100° = 180°
.
I
E
b.) m∠ICE
m∠ICE+m∠REC = 180°
.
m∠ICE = 180°-100°
m∠ICE = 80°

45. □RICE: Find the measurement of the following if m∠RIC=100°
R
C
.
I
E
c.) m∠ICR
.
m∠ICR = 1/2 m ∠ICE
m∠ICR = 1/2 (80)
m∠ICR = 40°

46. □RICE: Find the measurement of the following if the
m∠RIC=100° R
C
.
I
E
d.) m∠IEC
.
m∠IEC = 50°
m∠IEC = 1/2 m∠REC
m∠IEC = 1/2 (100)

48. . .
Solve for the unknown value of rhombus.
1. If EH = 21, HG = __________
2. If ∠EFG = 40°, ∠GFH = _________
3. If FH = 12, HI = _________
4. If ∠EHF = 8°, ∠EHG = _________

49. . .
Solve for the unknown value of rhombus.
If ∠HEG = 7x – 1 and ∠FEG = x + 11.
5. x = __________ 8. ∠EGH = __________
6. ∠HEG = __________ 9. ∠EFG = __________
7. ∠FEH = __________ 10. ∠EIH = __________

51. . .
Some of the brand logos make use of the
rhombus geometric shape. For instance, the logo
of Mitsubishi Motors Corporation, a Japanese
multinational automotive manufacturing company
comprises three rhombuses that are attached to
each other at one vertex.

52. . .
Let us use one of the rhombuses of
this brand logo.

57. Read each questions carefully.
Write the letter of the
correct answer.

58. .
>
>
.
1. In a rhombus ABCD, AB is 5.5
units. What is the measure of AD?
—
A. 3.5
B. 4.5
C. 5.5
D. 6.5
—

59. . .
2. How would you describe the
opposite angles in a rhombus?
A. Opposite angles are congruent.
B. Opposite angles have right angles.
C. Opposite angles are supplementary.
D. Opposite angles are equal to 𝟏𝟖𝟎°.

60. . .
3. In a rhombus, how would you
describe the diagonals?
B. Diagonals have right angles.
C. Diagonals are perpendicular.
D. Diagonals are supplementary.
A. Diagonals are congruent.

61. . .
4. What is the measurement of
BO?
—
A. 9
B. 10
C. 11
D. 12
12

62. . .
5. In rhombus SPEN below, what is
measure of SNE if mSPN is 𝟑𝟓°?
A. 𝟑𝟓°
B. 𝟓𝟓°
C. 𝟕𝟎°
D. 𝟏𝟏𝟎°
.
.
.
.
.
D

63. .
>
>
.
1. In a rhombus ABCD, AB is 5.5
units. What is the measure of AD?
—
A. 3.5
B. 4.5
C. 5.5
D. 6.5
—

64. . .
2. How would you describe the
opposite angles in a rhombus?
A. Opposite angles are congruent.
B. Opposite angles have right angles.
C. Opposite angles are supplementary.
D. Opposite angles are equal to 𝟏𝟖𝟎°.

65. . .
3. In a rhombus, how would you
describe the diagonals?
B. Diagonals have right angles.
C. Diagonals are perpendicular.
D. Diagonals are supplementary.
A. Diagonals are congruent.

66. . .
4. What is the measurement of
BO?
—
A. 9
B. 10
C. 11
D. 12
12

67. . .
5. In rhombus SPEN below, what is
measure of SNE if mSPN is 𝟑𝟓°?
A. 𝟑𝟓°
B. 𝟓𝟓°
C. 𝟕𝟎°
D. 𝟏𝟏𝟎°
.
.
.
.
.
D

68. ♥

69. 1. C
2. A
3. C
4. B
5. C