Unit 2 Quadrilaterals

Section 1 Types of angles

Name the congruent angles! 1, 4, 5, 7 2, 3, 6, 8

Different types of angles Vertical angles: 1 and 4, directly across from each other; always congruent Alternate interior angles: 3 and 6, inside the parallel lines on opposite sides of the transversal (form a “Z”) Congruent when lines are parallel Corresponding angles: 1 and 5. in the same place at each intersection Consecutive angles: 3 and 5, 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, ( 1 and 2)

Find the other angle measures. =120°

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°

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°

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

Section 2 Parallelograms & rhombuses

What is this called? PARALLELOGRAM!

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

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?

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?

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

Section 3 rectangles, squares, Trapezoids

SPECIAL QUADRILATERALS Trapezoid Quadrilateral Rhombus Square Parallelogram Rectangle

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?

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.)

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?

Example 2 Rectangle ABCD has angle ADB = 4x – 25 and angle DBC = x + 35. Find the measure of angle BDC.

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

EXAMPLE 3

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

EXAMPLE 4

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

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