Quadrilaterals Properties

2. 33 And the whole city was gathered together at the
door. 34 Then He healed many who were sick with
various diseases, and cast out many demons; and
He did not allow the demons to speak, because they
knew Him.35 Now in the morning, having risen a long
while before daylight, He went out and departed to
a solitary place; and there He prayed. 36 And Simon
and those who were with Him searched for Him. 37 When
they found Him, they said to Him, “Everyone is looking
for You.”
Mark 1: 33-39

3. 38 But He said to them, “Let us go into the
next towns, that I may preach there also,
because for this purpose I have come
forth.”
39 And He was preaching in their
synagogues throughout all Galilee,
and casting out demons.

4. QUADRILATERALS
“…geometric shapes are the
alphabet in which the book of
nature is written." -Galileo

5. Objectives
 Understand quadrilaterals.
 Determine the conditions that make a
quadrilateral a parallelogram.
 Discuss the properties of a parallelogram.
 Make distinct definitions of what
parallelograms, rectangles, squares, rhombi,
and trapezoids are.
 Construct a flow chart.

6. A quadrilateral is a
two-dimensional figure
formed by connecting
four segments through
its endpoints referred to
as vertices.
What is a
Quadrilateral?

7. Look around you, do you see
shapes that could be termed
as a quadrilateral?
What is a
Quadrilateral?

8. What are the types
of Quadrilaterals?

9. There are special
characteristics and
conditions that make
a quadrilateral a
parallelogram.

10. A quadrilateral with
both pairs of
opposite sides
parallel and equal
in length is known
as a parallelogram.

11. Properties of a
Parallelogram
Each diagonal of a parallelogram
divides the parallelogram into two
congruent triangles.
Opposite angles of a
parallelogram are congruent.
Opposite sides of a parallelogram
are congruent.

12. Any two consecutive angles of a
parallelogram are supplementary.
Properties of a
Parallelogram
If the diagonals of a quadrilateral
bisect each other, then it is a
parallelogram
A quadrilateral is a parallelogram
if two opposite sides are
congruent.

14. Midline Theorem
The segment that joins the
midpoints of two sides of a
triangle is parallel to the third
side and is one-half of its
measure.

16. 11 Then He said, “ Go out, stand on the mountain before
the Lord.” And behold, the Lord passed by, and a great
strong wind tore into the mountains and broke the rocks
in pieces before the Lord, but the Lord was not the wind;
and after the wind an earthquake, but the Lord was not in
the earthquake; 12 and after the earthquake a fire, but the
Lord was not in the fire; and after the fire a still small
voice.”
1 Kings 19: 11-12

17. Elijah personally challenges Ahab to a public contest
on Mt. Carmel to see who will accept a sacrifice by
fire -- Baal or Yahweh. On the appointed day, all
morning long and far into the afternoon, the
prophets of Baal try every way they can to get Baal
to answer them, but to no avail. Then Elijah builds an
altar and sacrifices a bull on it. Immediately, God's
fire falls and consumes the sacrifice -- and even the
stones of the altar. All the people fall to the ground
and acknowledge Yahweh as the true God. Elijah
slays the false prophets, and then calls on Yahweh to
end a three year drought.

18. Learning from God’s Still Small Voice.
1) God’s voice is not always quiet.
2) God’s voice is not always gentle.
Sometimes it comes to bring a strong
rebuke. (Acts 26:14)
3) God’s voice can provide comfort when
we are anxious.

19. The essence of the God’s nature
is not power --- though God is
fully capable of displaying power.
Rather, the essence of God is in
His relationship and
communication to the person.

20. SPECIAL PARALLELOGRAM

21. The three special parallelograms
are rectangle, rhombus and
square.

22. Name that Quadrilateral!
 A parallelogram with
four right angles.
 A parallelogram with
four congruent sides.
 A rectangle with four
congruent sides.

23.  Examples of shapes or curves that are
not classified as quadrilaterals. They do
not follow the definition of a quadrilateral.
Can you give a reason why?
Are They Quadrilaterals?
A
C
B

24. Since rectangles, rhombi, and
squares are parallelogram, all
properties of parallelogram apply
to these quadrilaterals.

25. The diagonals of a rectangle are
congruent.
If a parallelogram has at least one
right angle, then it is rectangle.
The diagonals of a rhombus are
perpendicular.
Each diagonal of a rhombus
bisects the opposite angles of the
rhombus.

26. If the diagonals of a
parallelogram are perpendicular
then the parallelogram is a
rhombus.
The diagonals of a square bisect
the vertex angle.

30. Venn Diagram shows relationships
• Each shape has the properties of every group that it
belongs to. For instance, a square is a rectangle, a
rhombus and a parallelogram; so it has all of the
properties of those shapes.
Rhombuses Rectangles
parallelograms
rhombi rectangles
squares
rhombi rectangles

31. Decide whether the
statement is always,
sometimes, or never true.
a.A rhombus is a
rectangle.
b.A parallelogram is a
rectangle.

32. Put the Information to Use…
 Given the information in the preceding
slides, construct a flow chart of the
different shapes.
 You should begin with the definition of a
quadrilateral, and work your way down
the chart.

35. Answer the following:
The angles of a quadrilateral ABCD taken
in an order are in the ratio 3 : 7 : 6 : 4.
Then ABCD is a
(a) kite
(b) parallelogram
(c) Rhombus
(d) trapezium

36. If the diagonals of a quadrilateral bisect
each other at right angles, it will be a
(a) Rhombus (b) Trapezium
(c) Rectangle (d) Kite

37. The sum of the angles of a quadrilateral is
(a) 180°
(b) 270°
(c) 360°
(d) 300°

38. In a square ABCD, the diagonals meet at
point O. The triangle AOB is
(a) isosceles right triangle
(b) equilateral triangle
(c) isosceles triangle but not right triangle
(d) scalene right triangle.

39. ABCD is a quadrilateral in which AB = 5 cm,
CD = 8 cm and the sum of angle A and angle
D is 180°. What is the name of this
quadrilateral?
(a) Parallelogram (b) Trapezium
(c) Rhombus (d) Can not be determined

40. Fill in the blanks.
The diagonals of a rhombus
bisect each other at _____
angles.

41. Try this!
1) The ratio of exterior angle to interior
angle of a regular polygon is 1:4. Find
the number of sides of the polygon.
2) Each interior angle of a polygon is 108°.
Find the number of sides of the
polygon.

42. 1) If three angles of a quadrilateral are
each equal to 75°, the fourth angle is
(a) 150° (b) 135° (c) 45° (d) 75°
2. For which of the following, diagonals
bisect each other?
(a) Square (b) Kite
(c) Trapezium (d) Quadrilateral
3. For which of the following figures, all
angles are equal?
(a) Rectangle (b) Kite
(c) Trapezium (d) Rhombus

43. 4. For which of the following figures,
diagonals are perpendicular to each other?
(a) Parallelogram (b) Kite
(c) Trapezium (d) Rectangle
5. For which of the following figures,
diagonals are equal?
(a) Trapezium (b) Rhombus
(c) Parallelogram (d) Rectangle

44. 6. Which of the following is a property of a
parallelogram?
(a) Opposite sides are parallel.
(b) The diagonals bisect each other at right
angles.
(c) The diagonals are perpendicular to each
other.
(d) All angles are equal.
7. What is the maximum number of obtuse
angles that a quadrilateral can have ?
(a) 1 (b) 2 (c) 3 (d) 4

45. 8. If two adjacent angles of a parallelogram
are (5x – 5)° and (10x +35)°, then the ratio
of these angles is
(a) 1 : 3
(b) 2 : 3
(c) 1 : 4
(d) 1 : 2