Quarter 3-Week 2.2-Theorems on Rhombus.pptx

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. Questions: 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 Given: Rhombus ROSE Prove:  

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

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

10. Proof: 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. REST is a rhombus. Find each missing value using the given information. If TE= 40 cm, find TQ If m = , find x.   2. is a square. If QI=x+5and FV = x+25, find EI.