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In the given parallelogram FACE, what does the segment connecting opposite vertices represent?

In the given parallelogram FACE, what does the segment connecting opposite vertices represent?. F A M E C. THE DIAGONALS OF A PARALLELOGRAM. OBJECTIVES:

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In the given parallelogram FACE, what does the segment connecting opposite vertices represent?

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  1. In the given parallelogram FACE, what does the segment connecting opposite vertices represent? F A M E C

  2. THE DIAGONALS OF A PARALLELOGRAM OBJECTIVES: 1.To show that the diagonals of a parallelogram bisect each other. 2. To solve problems involving diagonals of a parallelogram.

  3. CLASS ACTIVITY • PROCEDURE • Draw and cutout four parallelograms. Construct their diagonals. Let the name of the parallelograms be FACE with the diagonals intersecting at point M. 2. With a ruler, measure the distance from the vertex to the point of intersection of the two diagonals. 3. Record your observation.

  4. Data ( Group 1 )

  5. CRITICAL THINKING • Compare: FM and CM ; AM and EM. • Make a conjecture about the diagonals of a parallelogram F A M E C

  6. Guide Questions • In your activity, what can be said about the length of FM compare to the length of CM? How about the length of EM compare to the length of AM? • What segment that bisects FC? • What segment that bisects AE? • What can be said about the diagonals of a parallelogram?

  7. Rubric for the Group Activity

  8. THEOREM • THE DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER.

  9. STATEMENT Parallelogram FACE, with diagonals FC and AE. FA  CE REASON Given 2. Opposite sides of a //gram are congruent. Formal proof F A GIVEN: Parallelogram FACE with diagonals FC and AE 1 2 M E 3 4 PROVE: FM  CM ; AM  EM C PROOF:

  10. STATEMENT 3. FA// EC ;FE // AC 4. 1 4;2 3 5. FMA  CME 6. FM  CM AM  EM REASON 3. Definition of//gram 4. If 2 // lines are cut by a transversal, the alternate interior angles are congruent. 5. ASA Congruence 6. CPCTC Formal proof F A GIVEN: Parallelogram FACE with diagonals FC and AE 1 2 M E 3 4 PROVE: FM  CM ; AM  EM C PROOF:

  11. EXERCISES: A B • In the given figure, AD and BC are diagonals of //gram ABCD. O C D • AD = 10 cm, how long is BC? Ans.( 10 cm ) 2. If AB is 30 cm, how long is DC? Ans. ( 30 cm )

  12. EXERCISES: A B • In the given figure, AD and BC are diagonals of //gram ABCD. O C D 3. If AO = 15 cm, how long is CO? Ans.( 15 cm ) 4. If DO is 18 cm, how long is BO? Ans. ( 18 cm )

  13. 5. GIVEN: BS = 9x – 4 TS = 7x + 2 FIND : BT SOLUTION: Hence, BS = TS 9x – 4 = 7x +2 9X- 7X = 2 + 4 2X = 6 X = 3 BS = 23, TS = 23 Therefore, BT = 46 BATH is a parallelogram EXERCISES A B S H T

  14. 6. GIVEN: HS = 5x – 6 AS = 4x + 1 FIND : HA SOLUTION: Hence, HS = AS 5x – 6 = 4x +1 5X- 4X = 1 + 6 X = 7 HS = 29; AS = 29 Therefore, HA = 58 BATH is a parallelogram EXERCISES A B S H T

  15. EXERCISES: A B • In the given figure, AD and BC are diagonals of //gram ABCD. O C D 7. If AO= (3x-2)cm and CO= (x+8)cm, how long is AC? Ans.( 13 cm ) 8. If DB is 18 cm, how long is BO? Ans. ( 9 cm )

  16. GENERALIZATION • WHAT CAN BE SAID ABOUT THE DIAGONALS OF A PARALLELOGRAM?

  17. THEOREM • THE DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER.

  18. VALUING How do you relate this property of a parallelogram in our life? What moral lessons we can get out of this topic? L O I V E FAIRNESS IN DEALING WITH OTHERS.

  19. EVALUATION: R O • If RS + EO = 18 cm and ST = 5 cm, what is ET? • If RS + EO = 18 cm and ST = 5 cm, what is RS? • If RS = 2x-5 and RT =4, find x and the lengths of RS and ST. T E S GIVEN: Parallelogram ROSE with diagonals intersecting at point T.

  20. Agreement • Answer Test Yourself nos. 16 – 19, page 128. Geometry Textbook

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