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- 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. 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. 8.1 Angle Measures in PolygonsInterior Angles of a Quadrilateral –The sum of the measures of the interior angles of a quadrilateral is __________.
- 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. 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. 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. 8.1 Angle Measures in Polygons
- 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. 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. 8.2 Properties of ParallelogramsFind the values of x and y. D 15 E y° 53° G 4x-1 F
- 11. 8.2 Properties of ParallelogramsFind the values of x and y. D 16 E 10 2x 53° G y+2 F
- 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. 8.2 Properties of ParallelogramsSolve for the variable. D E 4(p+3)° 135° G F
- 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. 8.2 Properties of ParallelogramsSolve for PR, ST, and the measures of angles SRQ and PQR. P Q T S R
- 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. 8.3 Showing that a Quadrilateral is a ParallelogramGiven:Prove: ABCD is a parallelogram D E G F
- 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. 8.3 Showing that a Quadrilateral is a ParallelogramFor what value of x is quadrilateral DEFG a parallelogram? D E G F
- 20. 8.4 Properties of Rhombuses, Rectangles, and SquaresRhombus –Rectangle –Square –
- 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. 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. 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. 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. 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. 8.4 Properties of Rhombuses, Rectangles, and SquaresClassify the special quadrilateral. Explain your reasoning.
- 27. 8.4 Properties of Rhombuses, Rectangles, and SquaresSketch rhombus ABCD. List everything you know about it.
- 28. 8.4 Properties of Rhombuses, Rectangles, and SquaresSketch square ABCD. List everything you know about it.
- 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. 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. 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. 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. 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. 8.5 Using Properties of Trapezoids and KitesA ____________ is a quadrilateral that has two pairs of consecutive congruentsides, but opposite sides are __________________.
- 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. 8.5 Using Properties of Trapezoids and KitesIn the diagram, PQRS is a kite. Find Q P 83° 41° R S
- 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. 8.6 Identifying Special Quadrilaterals
- 39. 8.6 Identifying Special QuadrilateralsQuadrilateral ABCD has at least one pair of opposite angles congruent.What types of quadrilaterals meet this condition?
- 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. 8.6 Identifying Special QuadrilateralsWhat is the most specific name for quadrilateral DEFG? E D F G
- 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. 8.6 Identifying Special QuadrilateralsGive the most specific name for the quadrilateral. Explain your reasoning. A B D C
- 44. 8.6 Identifying Special QuadrilateralsGive the most specific name for the quadrilateral. Explain your reasoning. A B D C
- 45. 8.6 Identifying Special QuadrilateralsGive the most specific name for the quadrilateral. Explain your reasoning. A B D C
- 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.

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