Proves theorems on the different kinds of parallelogram.pptx

Proves theorems on the different kinds of parallelogram

1. Proves theorems on the different kinds of parallelogram (Rectangle, Rhombus, Square)

2. 5 minute drill Basics fundamental operations

3. Quadrilateral – a convex polygon with four sides Diagonal – a segment joining two non-consecutive vertices of a polygon. Parallelogram – a quadrilateral with both pairs of opposite sides parallel to each other. Rectangle – a parallelogram with a right angle. Rhombus – a parallelogram opposite equal acute angles, opposite equal obtuse angles and four equal sides. Square – a rectangle with two consecutive sides congruent – a rhombus with a right angle.

4. GEOMETRY MAGIC: TURN 2 CIRCLES INTO 1 SQUARE What you need: 2 paper strips of equal length Tape Scissors a passion for the thrill of mathematics

5. This lesson shall focus on theorems on the different kinds of parallelograms. RECTANGLE RHOMBUS SQUARE

6. RECTANGLE Theorem1: if a parallelogram has a right angle, then it has four right angles and the parallelogram is a rectangle Theorem 2: The diagonals of a rectangle are congruent. RHOMBUS Theorem 3: In a rhombus, the diagonals are perpendicular and they bisect each other. SQUARE Theorem 4: The diagonals of a square bisect each other, are congruent and perpendicular

7. Theorem 1. If a parallelogram has a right angle, then it has four right angles and the parallelogram is a rectangle Using the properties of a parallelogram, if ∠A is a right angle, then ∠B is also a right angle because ∠A and ∠B are supplementary angles. The same reasoning will prove that ∠C and ∠D are also right angles.

8. Theorem 2. The diagonals of a rectangle are congruent. Given:  BEST is a rectangle. ST = 24, BT = 7, and BS = 25 Find: a. ES b. BE c. ET d. m∠BES

9. Example 3: Given:  PICK is a rectangle. a. What kind of triangle is  KOC? Why? b. What kind of triangle is  PIC? Why? c. If PO + OI = 50, what is the measure of PC? d. Name all pairs of congruent segments in rectangle PICK.

10. Example 4: Given:  CORE is a rhombus a. Is CL = RL? Is EL = OL? b. Which triangles in  CORE are congruent? Why are they congruent?

11. Example 5: Given:  HINT is a rhombus What are the characteristics of  HINT?  

12. Example 6: Given:  ABCD is a rhombus. Find the measures of the numbered angles in the figure.  

13. Theorem 4. The diagonals of a square bisect each other, are congruent, and perpendicular

14. In a rectangle: Opposite sides are congruent Opposite sides are parallel Each diagonal separates the rectangle into two congruent triangles. Opposite angles are congruent. Consecutive angles are supplementary. All angles are right angles. Diagonals bisect each other and are congruent.

15. In a rhombus: All the sides are congruent. Opposite sides are parallel. Each diagonal separates the rhombus into two congruent triangles. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other and are perpendicular. Each diagonal bisects a pair of opposite angles.

16. In a square: All sides are congruent. All angles are right angles. Each diagonal separates the square into two congruent triangles. Opposite angles are congruent and supplementary. Consecutive angles are supplementary and are congruent. Diagonals bisect each other, are perpendicular, and congruent.

17. Assessment: (Post-Test) A. Answer the following statements with TRUE or FALSE. 1. A square is a rectangle. 2. A rhombus is a square. 3. A parallelogram is a square. 4. A rectangle is a rhombus. 5. A parallelogram is a square.

18. 6. A parallelogram is a rectangle. 7. A quadrilateral is a parallelogram. 8. A square is a rectangle and a rhombus. 9. An equilateral quadrilateral is a rhombus. 10. An equiangular quadrilateral is a rectangle.

19. B. Name all the parallelogram/s that possess/es the given. 1. All sides are congruent. 2. Diagonals bisect each other. 3. Consecutive angles are congruent. 4. Opposite angles are supplementary. 5. The diagonals are perpendicular and congruent.

20. THANK YOU, GRADE 9- LITHIUM! HOPE YOU LEARN SOMETHING FROM THIS LESSON!