Week 6 - Parallelogram - PART 2.pptx

1. QUADRILATERAL
Lesson 6

2. Parallelogram
LESSON 6
SLIDE
1. Show that both pairs of opposite sides are || . [definition]
2. Show that both pairs of opposite sides are  .
3. Show that one pair of opposite sides are both || and  .
4. Show that both pairs of opposite angles are  .
5. Show that the diagonals bisect each other .

3. Parallelogram
LESSON 6
SLIDE
Find the values of x and y that ensures the quadrilateral is a parallelogram.
6x = 4x + 8
2x = 8
x = 4
2y = y + 2
y = 2

4. Parallelogram
LESSON 6
SLIDE
Find the value of x and y that ensure the quadrilateral is a parallelogram.
2x + 8 = 120
2x = 112
x = 56
5y + 120 = 180
5y = 60
y = 12

5. Special Parallelogram
Lesson 6

6. Parallelogram
LESSON 6
SLIDE
A rectangle is a quadrilateral with four right angles.
• Is a rectangle is a parallelogram?
• Thus a rectangle has all the properties of a parallelogram.
 Yes, since opposite angles are congruent.

7. Properties of Rectangles
Parallelogram Properties:
 Opposite sides are parallel.
 Opposite sides are congruent.
 Opposite angles are congruent.
 Consecutive angles are supplementary.
 Diagonals bisect each other.
Plus:
 All angles are right angles.
 Diagonals are congruent.
 Also: ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles
triangles

8. Parallelogram
LESSON 6
SLIDE
8
1. If AE = 3x +2 and BE = 29, find the value of x.
2. If AC = 21, then BE = _______.
6
5
4
3
2
1
E
D C
B
A

9. Parallelogram
LESSON 6
SLIDE
9
1. If AE = 3x +2 and BE = 29, find the value of x.
E
D C
B
A

10. Parallelogram
LESSON 6
SLIDE
10
2. If AC = 21, then BE = _______.
E
D C
B
A

11. Parallelogram
LESSON 6
SLIDE
A square is a quadrilateral with four congruent angles
and four congruent sides.
• Opposite sides are parallel.
• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• Diagonals bisect each other.
Plus:
• Four right angles.
• Four congruent sides.
• Diagonals are congruent.
• Diagonals are perpendicular.
• Diagonals bisect opposite angles.
Since every square is a parallelogram as well as a rhombus and
rectangle, it has all the properties of these quadrilaterals.

12. Parallelogram
LESSON 6
SLIDE
Given: ABCD is a square. Complete the following.
1. If AB = 10, then AD = _____ and DC = _____.
2. If CE = 5, then DE = _____.
3. m<ABC = _____.
4. m<ACD = _____.
5. m<AED = _____.
8 7 6
5
4
3
2
1
E
D C
B
A
10 units 10 units
5 units
90°
45°
90°

13. Parallelogram
LESSON 6
SLIDE
A rhombus is a quadrilateral with four congruent sides.
• Since a rhombus is a parallelogram the following are true:
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
• Is a rhombus a parallelogram?
 Yes, since opposite sides are congruent.

14. Lesson 6-4: Rhombus & Square 14
Rhombus
Note: The four small triangles are congruent, by SSS.
This means the diagonals form
four angles that are congruent,
and must measure 90 degrees
each.
So the diagonals are perpendicular.
This also means the diagonals
bisect each of the four angles of
the rhombus
So the diagonals bisect opposite angles.

15. Properties of a Rhombus
.
Since a rhombus is a parallelogram the following are true:
• Opposite sides are parallel.
• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• Diagonals bisect each other.
Plus:
• All four sides are congruent.
• Diagonals are perpendicular.
• Diagonals bisect opposite angles.
• Also remember: the small triangles are RIGHT and CONGRUENT!

16. Parallelogram
LESSON 6
SLIDE
16
Given: ABCD is a rhombus. Complete the following.
1. If AB = 9, then AD = ______.
2. If m<1 = 65, the m<2 = _____.
3. m<3 = ______.
4. If m<ADC = 80, the m<DAB = ______.
5. If m<1 = 3x -7 and m<2 = 2x +3, then x = _____.
5
4
3
2
1
E
D C
B
A
9 units
65°
90°
100°
10

17. SLIDE
References
E-Math 9 - Work Text in Mathematics (Rex Book Store)
Math Ideas and Life Applications 9 - Second Edition (Abiva)
Spiral Math 9 – (Trinitas Publishing Inc.)
Parallelogram
LESSON 6