1. Unit 2
Quadrilaterals

2. Section 1
Types of angles

3. Name the congruent angles!
1, , ,
2, , ,

4. Different types of angles
Vertical angles: and , directly across from each other; always congruent
Alternate interior angles: and , inside the parallel lines on opposite sides of the transversal (form a “Z”)
Congruent when lines are parallel
Corresponding angles: and in the same place at each intersection
Consecutive angles: and , inside the parallel lines on the same side
Supplementary when lines are parallel
Supplementary = add up to 180°
Angles that form a line are also supplementary, ( and )

5. Find the other angle measures.
=120°

6. Measure of One Interior Angle Measure of One Exterior Angle
Angles of a polygon
Interior angles of a polygon add up to 180(n – 2)
n is the number of sides
Exterior angles of a polygon ALWAYS add up to 360°
Type of Polygon n
Sum of Interior Angles
Measure of One Interior Angle
Sum of Exterior Angles
Measure of One Exterior Angle
Triangle
Quadrilateral 3
180°
360° 4
360°
360°

7. Measure of One Interior Angle Measure of One Exterior Angle
Regular polygons
Regular polygon: polygon where all sides and angles are congruent
How do we find the measure of ONE angle on a regular polygon?
Divide the sum by the number of sides
Interior angle:
Exterior angle:
Type of Polygon n
Sum of Interior Angles
Measure of One Interior Angle
Sum of Exterior Angles
Measure of One Exterior Angle
Triangle 3
180°
360°
60°
120°

8. Wrap up
Exit Slip
Unit 2 Homework Packet Due Friday
Unit 2 Test Friday

9. Section 2
Parallelograms & rhombuses

10. What is this called?
PARALLELOGRAM!

11. Properties of a parallelogram
Opposite sides are parallel and congruent
Opposite angles are congruent
Diagonals bisect each other
Bisect = to split in half

12. Example 1
In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, AE = 2x + 8, and EC = 4x – 22. What is the value of x?
What do AE and EC form?
What do we know about the diagonals of a parallelogram?
What do we now know about AE and EC?
BONUS: Can you find the pairs of alternate interior angles and consecutive angles?

13. Example 2
In the accompanying diagram of parallelogram ABCD, diagonals AC and BD intersect at E, BE = ½x and ED = x – 4. What is the value of x?

14. wrap-up
Exit Slip
Unit 2 Homework Packet
Unit 2 Test

15. Section 3
rectangles, squares, Trapezoids

16. SPECIAL QUADRILATERALS
Trapezoid
Quadrilateral
Rhombus
Square
Parallelogram
Rectangle

17. rhombus A parallelogram with all four sides congruent
Has all the properties of a parallelogram, plus:
4 congruent sides
Diagonals are perpendicular
Food for thought：Are all rhombuses parallelograms? Are all parallelograms rhombuses?

18. EXAMPLE 1
PQRS is a rhombus. PQ = 2/3x and SP = 2x – 12. Find x. (Hint: Draw a sketch! You should always label the points of any figure in order.)

19. rectangle Parallelogram with four right angles
Has all the properties of a parallelogram, plus:
Four right angles
Congruent diagonals
Are all rectangles parallelograms? Are all parallelograms rectangles?

20. Example 2
Rectangle ABCD has angle ADB = 4x – 25 and angle DBC = x Find the measure of angle BDC.

21. SQUARE Parallelogram with four congruent sides and four right angles
Diagonals are congruent and perpendicular
Combination of a rhombus and a rectangle

22. EXAMPLE 3

23. TRAPEZOID Quadrilateral with only ONE pair of opposite sides parallel
Isosceles trapezoid
Legs (non-parallel sides) are congruent
Base angles are congruent
Diagonals are congruent

24. EXAMPLE 4

25. COMPARING QUADRILATERALS
Identify which shapes possess each property:
Shape
Four Sides
Opposite Sides Parallel
All Sides Congruent
Four Right Angles
Congruent Diagonals
Perpendicular Diagonals
Quadrilateral
Parallelogram
Rhombus
Rectangle
Square

26. Wrap up
Exit Slip
Unit 2 Test Monday
Unit 2 Homework Packet Due Monday