1. Prove A ≅ F Given parallelograms ABCD and CEFG… E F B C G A D
Unit 6 – Polygons and Quadrilaterals Conditions for Parallelograms
Given parallelograms ABCD and CEFG… A B C D E F G
Prove A ≅ F

2. Objective Determine if a quadrilateral is a parallelogram.
Unit 6 – Polygons and Quadrilaterals Conditions for Parallelograms
Objective
Determine if a quadrilateral is a parallelogram.

3. You have learned to identify the properties of a parallelogram.
Unit 6 – Polygons and Quadrilaterals Conditions for Parallelograms
You have learned to identify the properties of a parallelogram.
Now you will be given the properties of a quadrilateral and will have to decide if the quadrilateral is a parallelogram.
To do this, you can use the definition of a parallelogram or the conditions that follow.
REMINDER…the definition of a parallelogram is a quadrilateral with two pairs of opposite sides parallel.
REMEMBER…only one of the following conditions need to be met.

4. Conditions for a parallelogram.
Unit 6 – Polygons and Quadrilaterals Conditions for Parallelograms
Conditions for a parallelogram.
1. Both pairs of opposite sides are congruent.
2. Both pairs of opposite angles are congruent.
3. One pair of opposite sides are both congruent and parallel.
4. If the diagonals bisect each other.
5. If an angle is supplementary to both of its consecutive angles.

5. Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms
What values of x and y are necessary to make the figure a parallelogram?
(2y2-2)°
(139-2x)°
(3x+6y+25) °
(-5y+1)°

6. Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms
What values of a and b are necessary to make the figure a parallelogram?
2b-6
2a+10 4a
3a + 7

7. Unit 6 – Polygons and Quadrilaterals 6.3 Conditions for Parallelograms
What values of a and b are necessary to make the figure a parallelogram?
2a+b-8
(5a+2b+7)°
3a-30
(8a-3b)°

8. A quadrilateral has vertices A(2, 3), B(6, 2), C(5, 0), D(1, 1).
Unit 6 – Polygons and Quadrilaterals Conditions for Parallelograms
A quadrilateral has vertices A(2, 3), B(6, 2), C(5, 0), D(1, 1).
How could you show that quadrilateral ABCD is a parallelogram?

9. Objectives Vocabulary
Unit 6 – Polygons and Quadrilaterals Properties of Special Parallelograms
Objectives
Apply properties of rectangles, rhombuses, and squares.
Vocabulary
rectangle
rhombus
square

10. A rectangle is a quadrilateral with four right angles.
Unit 6 – Polygons and Quadrilaterals Properties of Special Parallelograms
A rectangle is a quadrilateral with four right angles.
Theorem:
The diagonals of a rectangle are congruent
AC  BD
If a quadrilateral is a rectangle, then it is a parallelogram

11. Prove the diagonals of a rectangle are congruent.
Unit 6 – Polygons and Quadrilaterals Properties of Special Parallelograms
Prove the diagonals of a rectangle are congruent.

12. The diagonals of a rhombus are perpendicular
Unit 6 – Polygons and Quadrilaterals Properties of Special Parallelograms
A rhombus is a quadrilateral with four congruent sides.
Theorems:
The diagonals of a rhombus are perpendicular
The diagonals of a rhombus bisect the angles
If a quadrilateral is a rhombus, then it is a parallelogram

13. TVWX is a rhombus. Find everything you can!
Unit 6 – Polygons and Quadrilaterals Properties of Special Parallelograms
TVWX is a rhombus. Find everything you can! 2 3 4

14. Unit 6 – Polygons and Quadrilaterals 6
Unit 6 – Polygons and Quadrilaterals Properties of Special Parallelograms
A square is a quadrilateral with four right angles and four congruent sides. A square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

15. POLYGONS QUADRILATERALS PARALELLOGRAMS RHOMBUS Opp sides congruent
4 sided figure
QUADRILATERALS
No pair of parallel sides.
2 pairs of adjacent congruent sides
1 pair of opp. sides parallel
2 pairs of opp. sides parallel
Opp sides congruent
Opp angles congruent
Diag. bisect each other
TRAPEZOID
PARALELLOGRAMS
KITE
4 congruent sides
4 right angles
Legs congruent
Diag perpendicular
One opp pair angles ≈
Other opp pair angles bisected by diag
ISOS. TRAPEZOID
RHOMBUS
RECTANGLE
Base angles congruent
Diagonals congruent
Legs congruent
Diag bisect angle
Diag perpendicular
Diag bisect angle
Diag perpendicular
Diag congruent
Diag congruent
SQUARE

16. HOMEWORK:
6.3(414): 11-14,17-19,21-23,35,36
6.4(424): 10-15,19-31(odds),40-42