1. 6-1: Intro to Quadrilaterals
Do NOW
Use the following diagram to solve: x y
x + y
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

2. 6-1: Intro to Quadrilaterals
Worksheet Key
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

3. 6-1: Intro to Quadrilaterals
Worksheet Key
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

4. 6-1: Intro to Quadrilaterals
Worksheet Key
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

5. 6-1: Intro to Quadrilaterals
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

6. Properties of Parallelograms
Section 6-2
Geometry PreAP, Revised ©2013
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

7. Properties of Parallelograms
If a quadrilateral is a parallelogram, then its opposite sides are congruent
The opposite sides are congruent
The opposite angles are congruent
The consecutive angles are supplementary
The diagonals bisect each other
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

8. 6-1: Intro to Quadrilaterals
Theorem 1
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
If PQRS is a parallelogram, then 𝑷𝑸 ≅ 𝑹𝑺 and 𝑸𝑹 ≅ 𝑷𝑺 .
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

9. 6-1: Intro to Quadrilaterals
Theorem 2
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
If PQRS is a parallelogram, then ∠𝑷≅∠𝑹 and ∠𝑸≅∠𝑺.
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

10. Theorem 3
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
If PQRS is a parallelogram, then 𝒙+𝒚=𝟏𝟖𝟎°.
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

11. 6-1: Intro to Quadrilaterals
Theorem 4
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

12. 6-1: Intro to Quadrilaterals
Example 1
Find the value of x and y that ensure the quadrilateral is a parallelogram. 6x
4x+8 y y²
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

13. 6-1: Intro to Quadrilaterals
Example 2
In Parallelogram CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF.
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

14. 6-1: Intro to Quadrilaterals
Your Turn
In Parallelogram CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find DF.
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

15. 6-1: Intro to Quadrilaterals
Example 3
WXYZ is a parallelogram. Find YZ.
YZ = XW
8a – 4 = 6a + 10
2a = 14
a = 7
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

16. 6-1: Intro to Quadrilaterals
Your Turn
WXYZ is a parallelogram. Find mZ.
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

17. Example 4
Determine if the quadrilateral must be a parallelogram. Justify your answer.
Yes. The 73° angle is supplementary to both its corresponding angles.
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

18. 6-3: Conditions of Parallelograms
Example 5
Determine if the quadrilateral must be a parallelogram. Justify your answer.
No. One pair of opposite angles are congruent. The other pair is not. The conditions for a parallelogram are not met.
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

19. Your Turn
Determine if the quadrilateral must be a parallelogram. Justify your answer.
Yes. The diagonal of the quadrilateral forms 2 triangles.
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

20. 6-3: Conditions of Parallelograms
Example 6
PQRS is a parallelogram for x = 10 and y = Find mS and mR
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

21. 6-3: Conditions of Parallelograms
Example 7
Solve for x and y of MLPN
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

22. 6-3: Conditions of Parallelograms
Your Turn
Solve for a and c of MLPN
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

23. Example 8
Three vertices of JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of vertex M. J K L J K L M
The coordinates of vertex M are (7, –4).
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

24. 6-3: Conditions of Parallelograms
Your Turn
Three vertices of PQRS are P(–3, –2), Q(–1, 4), and S(5, 0). Find the coordinates of vertex R.
2/5/2019 3:29 PM
6-3: Conditions of Parallelograms

25. 6-1: Intro to Quadrilaterals
Video
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals

26. 6-1: Intro to Quadrilaterals
Assignment
Pg 395: 15-24, 32-43, 46, 47 Pg 402: 11-15, 20-23
2/5/2019 3:29 PM
6-1: Intro to Quadrilaterals