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# Chapter 8 powerpoint 3

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### Chapter 8 powerpoint 3

1. 1. 8.1 Angle Measures in PolygonsIn a polygon, two vertices that are endpoints of the same side are called___________________________.A __________________ of a polygon is a segment that joins two nonconsecutivevertices.Diagonals from one vertex form __________________.
2. 2. 8.1 Angle Measures in PolygonsPolygon Interior Angles Theorem –The sum of the measures of the interior angles of a convex n-gon is ________________
3. 3. 8.1 Angle Measures in PolygonsInterior Angles of a Quadrilateral –The sum of the measures of the interior angles of a quadrilateral is __________.
4. 4. 8.1 Angle Measures in PolygonsFind the sum of the measures of the interior angles of a convex octagon.The sum of the measures of the interior angles of a convex polygon is 2340°. Classify thepolygon by the number of sides.
5. 5. 8.1 Angle Measures in PolygonsPolygon Exterior Angles Theorem –The sum of the measures of the exterior angles of a convex polygon, one angle at eachvertex is ______________
6. 6. 8.1 Angle Measures in PolygonsA convex hexagon has exterior angles with measures 34°, 49°, 58°, 67°, and 75°. What isthe measure of an exterior angle at the sixth vertex?
7. 7. 8.1 Angle Measures in Polygons
8. 8. 8.2 Properties of ParallelogramsA _____________________ is a quadrilateral with both pairs of opposite sides____________________.The term “parallelogram PQRS can be written as _____________.In _____________, ____________ and ____________ by definition.
9. 9. 8.2 Properties of ParallelogramsTheorem 8.3 –If a quadrilateral is a parallelogram, then its opposite sides are _________________.Theorem 8.4 –If a quadrilateral is a parallelogram, then its opposite angles are ________________.
10. 10. 8.2 Properties of ParallelogramsFind the values of x and y. D 15 E y° 53° G 4x-1 F
11. 11. 8.2 Properties of ParallelogramsFind the values of x and y. D 16 E 10 2x 53° G y+2 F
12. 12. 8.2 Properties of ParallelogramsTheorem 8.5 –If a quadrilateral is a parallelogram, then its consecutive angles are _________________.Solve for the variable. D E 42° 2x° G F
13. 13. 8.2 Properties of ParallelogramsSolve for the variable. D E 4(p+3)° 135° G F
14. 14. 8.2 Properties of ParallelogramsTheorem 8.6 –If a quadrilateral is a parallelogram, then its ______________ bisect each other. P Q T S R
15. 15. 8.2 Properties of ParallelogramsSolve for PR, ST, and the measures of angles SRQ and PQR. P Q T S R
16. 16. 8.3 Showing that a Quadrilateral is a ParallelogramTheorem 8.7 –If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a_________________.Theorem 8.8 –If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral isa ________________________. D E G F
17. 17. 8.3 Showing that a Quadrilateral is a ParallelogramGiven:Prove: ABCD is a parallelogram D E G F
18. 18. 8.3 Showing that a Quadrilateral is a ParallelogramTheorem 8.9 –If one pair of opposite sides of a quadrilateral are __________________________, thenthe quadrilateral is a _________________.Theorem 8.10–If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a________________________. D E G F
19. 19. 8.3 Showing that a Quadrilateral is a ParallelogramFor what value of x is quadrilateral DEFG a parallelogram? D E G F
20. 20. 8.4 Properties of Rhombuses, Rectangles, and SquaresRhombus –Rectangle –Square –
21. 21. 8.4 Properties of Rhombuses, Rectangles, and SquaresRhombus Corollary – A quadrilateral is a rhombus if and only if it has_____________________________.Rectangle Corollary – A quadrilateral is a rectangle if and only if it has_____________________________.Square Corollary – A quadrilateral is a square if and only if it is a _____________and a ____________________.
22. 22. 8.4 Properties of Rhombuses, Rectangles, and SquaresFor any rectangle ABCD, decide whether the statement is always or sometimestrue. Draw a sketch and explain your reasoning.a.b.
23. 23. 8.4 Properties of Rhombuses, Rectangles, and SquaresFor any rhombus ABCD, decide whether the statement is always, sometimes, ornever true. Draw a sketch and explain your reasoning.a.b.
24. 24. 8.4 Properties of Rhombuses, Rectangles, and SquaresDiagonal Theorems –Theorem 8.11 –A parallelogram is a rhombus if and only if its diagonals are _____________________Theorem 8.12 –A parallelogram is a rhombus if and only if each diagonal ___________________ apair of opposite angles.Theorem 8.13 –A parallelogram is a rectangle is and only if its diagonals are ____________________
25. 25. 8.4 Properties of Rhombuses, Rectangles, and SquaresFor any rhombus DEFG, decide whether the statement is always, sometimes, or nevertrue. Draw a sketch and explain your reasoning.
26. 26. 8.4 Properties of Rhombuses, Rectangles, and SquaresClassify the special quadrilateral. Explain your reasoning.
27. 27. 8.4 Properties of Rhombuses, Rectangles, and SquaresSketch rhombus ABCD. List everything you know about it.
28. 28. 8.4 Properties of Rhombuses, Rectangles, and SquaresSketch square ABCD. List everything you know about it.
29. 29. 8.5 Using Properties of Trapezoids and KitesA _________________ is a quadrilateral with exactly one pair of parallel sides.These parallel sides are called the __________________.For each of the bases, there is a pair of _____________________________.The nonparallel sides are called the _________________.If the legs are congruent, then the trapezoid is an _______________________.
30. 30. 8.5 Using Properties of Trapezoids and KitesShow that ABCD is a trapezoid.A (1,2), B (4,5), C (7,3), D (7,-2)
31. 31. 8.5 Using Properties of Trapezoids and KitesTheorem 8.14 –If a trapezoid is isosceles, then each pair of base angles is __________________.Theorem 8.15 –If a trapezoid has a pair of congruent base angles, then it is an _______________trapezoid.Theorem 8.16 –A trapezoid is isosceles if and only if its diagonals are __________________.
32. 32. 8.5 Using Properties of Trapezoids and KitesTheorem 8.17 Midsegment Theorem for Trapezoids –The midsegment of a trapezoid is ________________ to each base and itslength is ______________ the sum of the lengths of the bases. A B P Q D C
33. 33. 8.5 Using Properties of Trapezoids and KitesIn this diagram, ABCD is an isosceles trapezoid, and PQ is the midsegment.a. Findb. Find A B P Q D C
34. 34. 8.5 Using Properties of Trapezoids and KitesA ____________ is a quadrilateral that has two pairs of consecutive congruentsides, but opposite sides are __________________.
35. 35. 8.5 Using Properties of Trapezoids and KitesTheorem 8.18 –If a quadrilateral is a kite, then its diagonals are ______________________.Theorem 8.19 –If a quadrilateral is a kite, then exactly one pair of opposite angles are ____________. C CB D B D A A
36. 36. 8.5 Using Properties of Trapezoids and KitesIn the diagram, PQRS is a kite. Find Q P 83° 41° R S
37. 37. 8.5 Using Properties of Trapezoids and KitesIn a kite, the measures of the angles are 6x°, 24°, 84°, and 126°. Find the value of x.What are the measures of the angles that are congruent?
38. 38. 8.6 Identifying Special Quadrilaterals
39. 39. 8.6 Identifying Special QuadrilateralsQuadrilateral ABCD has at least one pair of opposite angles congruent.What types of quadrilaterals meet this condition?
40. 40. 8.6 Identifying Special QuadrilateralsQuadrilateral WXYZ has at least one pair of opposite sides that are parallel.What types of quadrilaterals meet this condition?
41. 41. 8.6 Identifying Special QuadrilateralsWhat is the most specific name for quadrilateral DEFG? E D F G
42. 42. 8.6 Identifying Special QuadrilateralsIs enough information given in the diagram to show that quadrilateral ABCDis a rhombus? Explain. B A C D
43. 43. 8.6 Identifying Special QuadrilateralsGive the most specific name for the quadrilateral. Explain your reasoning. A B D C
44. 44. 8.6 Identifying Special QuadrilateralsGive the most specific name for the quadrilateral. Explain your reasoning. A B D C
45. 45. 8.6 Identifying Special QuadrilateralsGive the most specific name for the quadrilateral. Explain your reasoning. A B D C
46. 46. 8.6 Identifying Special QuadrilateralsYou are given the following information about quadrilateral ABCD.Is enough information given to conclude that quadrilateral ABCD is atrapezoid? Explain.