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Geometry Concepts Explored & Applied

Explore various geometric concepts, angles, polygons, and quadrilaterals through examples and calculations. Learn about interior and exterior angles, segment congruence, diagonals, and more to deepen your understanding of geometry.

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Geometry Concepts Explored & Applied

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  1. Write the inverse:Is it true or false? If an animal is not a panda, then it is not black and white. (False—zebra) If an animal is a panda, then it is black and white.

  2. A Which angle is the smallest? Which side is the shortest? 41˚ 82˚ B C 57˚ <C, side AB

  3. Find the sum of the interior angles of a: 14(180) = 2520˚ 16-gon

  4. Find the measure of one interior angle of a regular: 6(180) = 135˚ 8 Octagon

  5. Which quadrilaterals have: IT 1 pair of opposite sides congruent

  6. Find the measure of one exterior angle of a regular: 360 = 72˚ 5 Pentagon

  7. Find the measure of one exterior angle of a regular: 360 = 18˚ 20 20-gon

  8. Find the sum of the exterior angles of a: 360˚ 20-gon

  9. Which quadrilaterals have: R, S, IT Congruent diagonals

  10. Find the midpoint: AVERAGE!! (5.5, 7) (3, 5) (8, 9)

  11. Which quadrilaterals have: Rh, S Perpendicular diagonals

  12. Which quadrilaterals have: Trapezoid 1 pair of opposite sides //

  13. Which quadrilaterals have: P, R, Rh, S 2 pairs of opposite sides congruent

  14. Find the measure of one exterior angle of a regular: 360 = 45˚ 8 Octagon

  15. Find the sum of the exterior angles of a: 360˚ 37-gon

  16. Find the sum of the interior angles of a: 4(180) = 720˚ Hexagon

  17. A 50˚ 180 – 50 = 130 130 /2 = 65 Which angle is the smallest? Which side is the shortest? 65˚ 65˚ B C <A, side BC

  18. Which quadrilaterals have: P, R, Rh, S Diagonals that bisect each other

  19. 72˚ 180 – 72 = 108 108 /2 = 54 Find the measure of angle J J 54˚

  20. Write a biconditional: Two segments are congruent iff they have the same length. If 2 segments are congruent, then they have the same length.

  21. Which quadrilaterals have: P, R, Rh, S Opposite angles congruent

  22. Find the sum of the exterior angles of a: 360˚ septagon

  23. Write a biconditional: A polygon is a hexagon iff it has 6 sides. If a polygon is a hexagon, then it has 6 sides.

  24. Find the distance: 52 + 42 = d2 25 + 16 = d2 41 = d2 6.40 ≈ d (3, 5) (8, 9)

  25. Find the midpoint: AVERAGE!! (-8.5, 3) (-9, 7) (-8, -1)

  26. Find the measure of one interior angle of a regular: 3(180) = 108˚ 5 Pentagon

  27. Write the converse:Is it true or false? If an animal is black and white, then it is a panda. (False—zebra) If an animal is a panda, then it is black and white.

  28. Find the distance: 12 + 82 = d2 1 + 64 = d2 65 = d2 8.06 ≈ d (-9, 7) (-8, -1)

  29. Find the midpoint: AVERAGE!! (7, 0) (10, -4) (4, 4)

  30. Find the measure of one exterior angle of a regular: 360 = 36˚ 10 Decagon

  31. Find the sum of the exterior angles of a: 360˚ nonagon

  32. Find the distance: 122 + 52 = d2 144 + 25 = d2 169 = d2 13 = d (-2, 3) (10, -2)

  33. Find the midpoint: AVERAGE!! (4, ½) (-2, 3) (10, -2)

  34. Which quadrilaterals have: Rh, S Diagonals that bisect angles

  35. Write a biconditional: A quadrilateral has both pairs of opposite sides congruent iff it is a parallelogram. If a quadrilateral has both pairs of opposite sides congruent, then it is a parallelogram.

  36. Find the distance: 72 + 242 = d2 49 + 576 = d2 625 = d2 25 = d (2, -10) (-5, 14)

  37. Find the midpoint: AVERAGE!! (-1.5, 2) (2, -10) (-5, 14)

  38. 59 + 72 = 131 180 – 131 = 49 Find the measure of angle J 72˚ J 59˚ 49˚

  39. Write the contrapositive:Is it true or false? If an animal is not black and white, then it is not a panda. (True) If an animal is a panda, then it is black and white.

  40. Find the sum of the interior angles of a: 10(180) = 1800˚ Dodecagon

  41. A (x + 2)˚ x + x – 2 + x + 2 = 180 3x = 180 x = 60 Which angle is the smallest? Which side is the shortest? 62˚ 58˚ 60˚ (x – 2)˚ B C x˚ <B, side AC

  42. Find the measure of one interior angle of a regular: 14(180) = 157.5˚ 16 16-gon

  43. Find the distance: 62 + 82 = d2 36 + 64 = d2 100 = d2 10 = d (10, -4) (4, 4)

  44. (5x + 1)˚ 5x + 1 + 3x + 3 + 3x = 180 11x + 4 = 180 11x = 176 x = 16 Find the measure of angle J (3x + 3)˚ J (3x)˚ 3(16) + 3 = 52˚

  45. Which quadrilaterals have: P, R, Rh, S 2 pairs of opposite sides //

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