Proves theorems on the different kinds of parallelogram

1. Provestheoremsonthedifferent
kindsofparallelogram
(Rectangle,Rhombus, Square)

2. 5MINUTEDRILL
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

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

15. In a rectangle:
1.Opposite sides are congruent
2.Opposite sides are parallel
3.Each diagonal separates the rectangle into
two congruent triangles.
4.Opposite angles are congruent.
5.Consecutive angles are supplementary.
6.All angles are right angles.
7.Diagonals bisect each other and are
congruent.

16. In a rhombus:
1.All the sides are congruent.
2.Opposite sides are parallel.
3.Each diagonal separates the rhombus into
two congruent triangles.
4.Opposite angles are congruent.
5.Consecutive angles are supplementary.
6.Diagonals bisect each other and are
perpendicular.
7.Each diagonal bisects a pair of opposite

17. In a square:
1.All sides are congruent.
2.All angles are right angles.
3.Each diagonal separates the square into
two congruent triangles.
4.Opposite angles are congruent and
supplementary.
5.Consecutive angles are supplementary and
are congruent.
6.Diagonals bisect each other, are

18. 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.

19. 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.

20. 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.

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