1. A man and his wife have three sons, and every one of the sons has a sister…
How many people are there in the family?
A B C D. 12

2. Warm up Identify the transformation ∆RST → ∆XYZ.
Is XY congruent to RS?
What is the length of XY?

3. Types of Quadrilaterals (4-sided figures)

4. A four sided figure with both pairs of opposite sides parallel
Parallelograms
A four sided figure with both pairs of opposite sides parallel

5. Skills Check
Do you know these?

6. Some Special Properties of Parallelograms
Opposite sides are congruent in length
Diagonals bisect each other
Both pairs of opposite sides are parallel

7. To Prove Parallel (use slope formula)
Means opposite sides have the SAME SLOPE
Sides Congruent (use distance formula)
Means their distances are the same

8. Solve for x.

9. Solve for x.

10. A parallelogram with 4 right angles
Rectangle
A parallelogram with 4 right angles

11. Some Special Properties of Rectangles
All the properties of a parallelogram
Diagonals are congruent
4 right angles

12. To Prove Opposite Sides Congruent (use distance formula)
Parallel (use slope formula)
Means opposite sides have the SAME SLOPE
4 Right Angles (use slope formula)
Means consecutive sides have opposite reciprocal slopes
Opposite Sides Congruent (use distance formula)
Means opposite sides have the same distance

13. A parallelogram with 4 congruent sides
Rhombus
A parallelogram with 4 congruent sides

14. Some Special Properties of Rhombus
All the properties of a parallelogram
Diagonals are perpendicular
4 congruent sides

15. To Prove Sides Congruent (use distance formula)
Parallel (use slope formula)
Means opposite sides have the SAME SLOPE
Perpendicular (use slope formula)
Means diagonals have opposite reciprocal slopes
Sides Congruent (use distance formula)
Means their distances are the same

16. Solve for x in this rhombus.

17. Rhombus VY = 2. mZVY Z

18. A parallelogram with 4 congruent sides & 4 right angles
Square
A parallelogram with 4 congruent sides & 4 right angles

19. Some Special Properties of Square
All the properties of a parallelogram, rectangle, & rhombus

20. Solve for x in this square.

21. Square 1. EJ = 2. HF = 3. mEJF 4. mHGF

22. Kite
A quadrilateral with 2 pairs of consecutive congruent sides, but opposites sides are NOT parallel

23. Some Special Properties of Kite
Diagonals are perpendicular

24. To Prove 2 Pairs of Consecutive Sides Congruent (use distance formula)
Not Parallel (use slope formula)
All sides have a different slope
2 Pairs of Consecutive Sides Congruent (use distance formula)
Means two pair of sides have the same distance

25. A quadrilateral with 1 pair of parallel sides called bases
Trapezoid
A quadrilateral with 1 pair of parallel sides called bases

26. Have only one pair of opposite sides that are parallel.
Trapezoids
Have only one pair of opposite sides that are parallel.
base
leg

27. Isosceles Trapezoid
A quadrilateral with 1 pair of parallel sides called bases and non-parallel sides are congruent (legs)

28. Some Special Properties of Isosceles Trapezoid
Diagonals are congruent

29. To Prove Bases Parallel (use slope formula)
Means 1 pair of opposite sides have the SAME SLOPE
Legs Congruent (use distance formula)
Means their distances are the same
Diagonals Congruent (use distance formula)

30. Classifying Triangles by Sides
Equilateral – 3 congruent sides
Isosceles – 2 congruent sides
Scalene – No sides congruent

31. To Prove Congruent (use distance formula)
Means their distances are the same; figure out how many sides of the triangle have the same distance

32. Find the Missing Point Worksheet
Classwork
Find the Missing Point Worksheet

33. Quadrilaterals and Parallelograms Homework Worksheet