this pesentation is for grade 9

1. Pulo National High School
WELCOME
to
MATHEMATICS 9
CLASS !
Gina Acayen-Trinidad
Teacher

2. LESSON TITLE :
Theorems
on
Rhombus

3. Objectives:
At the end of the lesson the students
should be able to :
 proves theorem on rhombus
 apply theorems on rhombus
 recognize the importance and the
uses of theorems of rhombus in
dealing with real-life situations

4. Group
Activity#3:
Activity 8 : I Wanna
Know More !
Page 322-323 of the
Math Book
10
minutes

5. Questi
ons:
1. Compare the measures of and What
did you observe?
2. What does do to ? Why?
3. Compare the measures of and . What
did you observe?
4. What does do to ? Why??
5. Compare the measures of and ? What
did you observe?

6. The diagonals of a rhombus are
perpendicular.
Theorem 3
Give
n:
Rhombus ROSE
Prove:

7. Proo
f: Statements Reasons
1. Rhombus ROSE 1. Given
2. 2. Definition of rhombus
3. and 3. The diagonals of a parallelogram bisect each other.
4. 4.
5. 5. Definition of midpoint
6. 6. Reflexive Property
7. SSS Congruence Postulate
7.

8. Con
t. Statements Reasons
8. 8. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
9. are right angles 9. form a linear pair and are
∠𝑅𝐻𝑂 𝑎𝑛𝑑 ∠𝑆𝐻𝑂
congruent
10. 10. Perpendicular lines meet to form right angles

9. Each diagonal of a rhombus bisects
opposite angles.
Theorem 4
Give
n:
Rhombus VWXY
Prove: ≌
≌

10. Proo
f: Statements Reasons
1. 1. Given
2. ≌ 2. Definition of rhombus (All sides are equal)
3. 3. Theorem 1
4. ≌ 4. Reflexive Property
5. 5. SSS Congruence Postulate/Property 5
6. CPCTC
6. 1 2; 3
∠ ≌ ∠ ∠ ≌
4
∠

11. Summary of the Properties of
Rhombus
• All sides are congruent.
• Opposite sides are parallel and congruent
• Opposite angles are congruent.
• Diagonals bisect each other.
• Diagonals are perpendicular.
• Diagonals bisect vertices
• Consecutive angles are supplementary.
• Each of the diagonal divides the rhombus
into two congruent triangles

12. Direction: Do as indicated.
If QUAD is a rhombus
1. QD = 15, DA= ____
2. DU =23,EU =____
3. QE=16.5, QA = ____
4. m QEU = ____
∠
5. m QDA =124
∠ ֯ ,
m QDU = ____
∠

13. Apply the different properties of
rhombus by solving the problem below.
1. REST is a rhombus. Find each missing
value using the given information.
a. If TE= 40 cm, find TQ
b. If m= , find x.
2. is a square. If QI=x+5and FV = x+25,
find EI.