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Warmup 6-1

Warmup 6-1. On a half piece of paper find the midpoint, distance, and slope for each. (2, 5), (6, 17) (-2, 3), (4, 6) (7, -3), (4, 10). …answers. Midpoint (4, 11) Distance = 12.6 Slope = 3 Midpoint (1, 4.5) Distance = 6.7 Slope = ½ Midpoint (5.5, 3.5) Distance = 13.3

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Warmup 6-1

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  1. Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. • (2, 5), (6, 17) • (-2, 3), (4, 6) • (7, -3), (4, 10)

  2. …answers • Midpoint (4, 11) Distance = 12.6 Slope = 3 • Midpoint (1, 4.5) Distance = 6.7 Slope = ½ • Midpoint (5.5, 3.5) Distance = 13.3 Slope = -4.3 (-13/3) We will have a quiz on Midpoint, Distance, Slope!

  3. Lesson 6-1: Quadrilaterals Vocab Quadrilateral Opposite Consecutive

  4. Quadrilateral→ any 4-sided figure • Opposite • Opposite sides → do not touch • Opposite angles → diagonal to each other • Consecutive (Adjacent) • Consecutive sides → touch • Consecutive angles → share a side

  5. Name opposite and consecutive sides and angles. B 2 A 1 3 D 4 C Opposite sides: AB & CD; BC & AD Consecutive sides: AB & BC; AB & AD; CD & BC; CD & AD Opposite angles: Angles 1 & 4; and 2 & 3 Consecutive angles: Angles 1 & 2; 1 & 3; 2 & 4; 3 & 4

  6. Types of Quadrilaterals Quadrilateral 2 pairs of parallel, opposite sides No parallel sides 1 pair of parallel, opposite sides Parallelogram Kite Trapezoid Rectangle Rhombus Each shape will have any properties of shape above it! Square

  7. Quadrilateral Relationships Quadrilaterals Parallelograms Trapezoids Rectangles Rhombi Squares Kites

  8. 6-1 Problems • Determine the figure by looks • Determine the figure by calculations • Find length of opposite sides → distance formula • Find slope of opposite sides → slope formula • Find the missing value • Set opposite sides equal → solve • Consecutive angles add to 1800 → solve

  9. Midpoint, Distance, Slope Quiz 1 On a piece of paper find the midpoint, distance, and slope for each. • (-1, 3), (0, 5) • (4, -2), (8, -5) • (3, 5), (6, 14)

  10. Quiz 1…answers • Midpoint (-0.5, 4) Distance = 2.2 Slope = 2 • Midpoint (6, -3.5) Distance = 5 Slope = -3/4 or -0.75 • Midpoint (4.5, 9.5) Distance = 9.5 Slope = 3

  11. Properties of Quadrilaterals • Review handout

  12. Foldable 1. Take out a piece of notebook paper fold the right edge over to the pink line.

  13. The fold crease Foldable 2. Now, divide the right hand section into 4 sections by drawing 3 evenly spaced lines. 3. Use scissors to cut along your drawn line, but ONLY to the crease!

  14. The fold crease Foldable 4. Write PARALLELOGRAMS down the left hand side ParallelOgrams

  15. The fold crease Foldable 5. Fold over the top cut section and write PARALLELOGRAM on the outside. Parallelogram 6. Reopen the fold. Parallelograms

  16. Foldable 7. On the left hand section, draw a parallelogram. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary 8. On the right hand side, list all of the properties of a parallelogram. Parallelograms 9. Place in your notebook and save for tomorrow.

  17. Foldable * Fold over the second cut section and write RECTANGLE on the outside. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * Reopen the fold. RECTANGLE Parallelograms

  18. Foldable * On the left hand section, draw a rectangle. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * On the right hand side, list all of the properties of a rectangle. 1. Properties of a parallelogram. 2. Has a right angle 3. Diagonals are congruent. Parallelograms

  19. Foldable * Fold over the third cut section and write RHOMBUS on the outside. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary 1. Properties of a parallelogram. 2. Has a right angle 3. Diagonals are congruent. * Reopen the fold. Parallelograms RHOMBUS

  20. Foldable * On the left hand section, draw a rhombus. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * On the right hand side, list all of the properties of a rhombus. 1. Properties of a parallelogram. 2. Has a right angle 3. Diagonals are congruent. Parallelogram 1. Properties of a parallelogram 2. Has 4 Congruent sides 3. Diagonals are perpendicular. 4. Diagonals bisect opposite angles

  21. Foldable * Fold over the third cut section and write SQUARE on the outside. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary 1. Properties of a parallelogram. 2. Has a right angle 3. Diagonals are congruent. * Reopen the fold. Parallelograms 1. Properties of a parallelogram 2. Has 4 Congruent sides 3. Diagonals are perpendicular. 4. Diagonals bisect opposite angles SQUARE

  22. Foldable * On the left hand section, draw a square. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * On the right hand side, list all of the properties of a square. 1. Properties of a parallelogram. 2. Has a right angle 3. Diagonals are congruent. Parallelograms 1. Properties of a parallelogram 2. Has 4 Congruent sides 3. Diagonals are perpendicular. 4. Diagonals bisect opposite angles 1. Is a parallelogram, rectangle, and rhombus 2. 4 congruent sides and 4 congruent (right) angles

  23. Lesson 6-2/6-3: Parallelograms(Put on back of foldable) • Proving a parallelogram • 2 pairs of opposite sides congruent • 2 pairs of opposite sides parallel • 1 pair of opposite sides congruent & parallel • Diagonals bisect each other • 2 pairs of opposite angles congruent

  24. Using Alternate Interior Angles • If you have a parallelogram, then any diagonal is a _______________ • ______________________ are created by the diagonal like angles ____ and ____ • THESE ANGLES _______________________ Remember this diagram?

  25. Using Alternate Interior Angles transversal • If you have a parallelogram, then any diagonal is a • are created by the diagonal like angles and • THESE ANGLES Remember this diagram? 1 2 Alternate interior angles 1 2 MUST BE CONGRUENT

  26. 6-2/6-3 Problems • Apply properties of parallelograms • Set opposite sides equal to each other • Set parts of diagonal equal to each other • Set opposite angles equal to each other • Consecutive angles add to 1800

  27. Midpoint, Distance, Slope Quiz 2 On a piece of paper find the midpoint, distance, and slope for each. • (4, -2), (0, 3) • (12, 15), (20, 2) • (10, 5), (10, 16)

  28. Quiz 2…answers • Midpoint (2, 0.5) Distance = 6.4 Slope = -5/4 or -1.25 • Midpoint (16, 8.5) Distance = 15.3 Slope = -13/8 or -1.625 • Midpoint (10, 10.5) Distance = 11 Slope = 0

  29. 6-4 Special Parallelograms • Apply properties of rectangles, rhombi, and squares • Know diagonal properties • Diagonals bisect each other → all • Diagonals equal → rectangle & square • Diagonals perpendicular → rhombus & square • Diagonals bisect angles → rhombus & square • Area of a rhombus:

  30. Lesson 6-5Trapezoids & Kites

  31. Trapezoids • Trapezoid Properties • 1 pair of _______________ • 2 pairs of consecutive (adjacent) angles are ___________ → pairs that touch the same ______ • ____________ Trapezoid • All properties of a__________ • Legs are __________ • Base angles (angles touching the same base) are ________ • Diagonals are___________ • __________ Trapezoid • All properties of a____________ • Has a ________ angle

  32. Kite • Properties • 2 pairs of consecutive (adjacent) sides__________ • 1 diagonal is ___________ • Diagonals are _________________ • 1 diagonal is an _________________

  33. Trapezoids 1200 parallel sides 600 supplementary • Trapezoid Properties • 1 pair of • 2 pairs of consecutive (adjacent) angles are → pairs that touch the same • Trapezoid • All properties of a • Legs are • Base angles (angles touching the same base) are • Diagonals are • Trapezoid • All properties of a • Has a angle legs Isosceles trapezoid congruent congruent congruent Right trapezoid right

  34. Kite congruent • Properties • 2 pairs of consecutive (adjacent) sides • 1 diagonal is • Diagonals are • 1 diagonal is an bisected perpendicular (900) angle bisector

  35. 6-5 Problems • Know the properties of trapezoids & kites • Use angle relationships • Trapezoids: angles between parallel sides are supplementary (add to 1800) • Kites: diagonals are perpendicular (900)

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