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Geometry Questions: Angles, Lines, and Shapes

Test your knowledge of angles, lines, and shapes with these geometry questions. Determine which statements are true and improve your geometry skills.

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Geometry Questions: Angles, Lines, and Shapes

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  1. Area and perimeter Angles Algebra 1 2 3 Triangles Statistics Probability 4 6 5 Bearings Graphs Solids 8 7 9

  2. Angles Foundation Higher

  3. Lines AB and CD are parallel. EF is perpendicular to AB. Angle FAE = 47o B E D 47o A F C Statements Angle AFC is 47o EF is perpendicular to CD Angle AFE is 47o Check Which statements are true?

  4. Back Similar Question Statements 1 & 2 are true Statement 3 is false. Angle AFE = 43o Did you get it right? Home

  5. B E Lines AB and CD are parallel. AF = AE. Angle AFE = 70o D A 70o F Statements Angle FAE is 40o Angle EFD = 70o Angle AFC is 40o C Check Which statements are true?

  6. Back All 3 statements are true. Did you get it right? Home

  7. Chords AD and CB intersect at the centre of the circle, O. Angle CDA = 35o B A O D 35o • Statements • Angle BCD = 35o • Angle CBD = 55o • Angle AOC = 70o C Check Which statements are true?

  8. Back Similar Question All three statements are true. Choose a new starter Home

  9. Chords AD and CB intersect at point E. Angle CDA = 40o B A E D 40o • Statements • Angle DAB = 40o • Angle ABC = 40o • Angle AEC = 80o C Check Which statements are true?

  10. Back Statement 1 is false because the lines AB and CD are not parallel Statement 2 is true (angles on same arc) Statement 3 is false because E is not the centre of the circle Choose a new topic Home

  11. Area & Perimeter Foundation Higher

  12. This large rectangle is made from 4 smaller rectangles, each measuring 2cm by 4cm • Statements • The perimeter of a small rectangle is 12cm • The perimeter of the large rectangle is 48cm • The area of the large rectangle is 24cm2 Which statements are true? Check

  13. Back Similar Question Only statement 1 is true. The large rectangle measures 8cm by 4cm so its perimeter is 24cm and its area is 32cm2 Well done if you got it right Home

  14. This shape is made from 6 rectangles, each measuring 3cm by 5cm and a red rectangle • Statements • The perimeter of the red rectangle is 18cm • The area of the red rectangle is 14cm2 • Less than 10% of the whole shape is red. Which statements are true? Check

  15. Back Statements 1 & 2 are true. Statement 3 is not accurate. Over 13% is red. Well done if you got it right Home

  16. ABCD is a trapezium. AB = AD = 3cm DC = 7cm BAD = ADC = 90o 3cm A B 3cm C D 7cm • Statements • The area of the trapezium is 15cm2 • BC is 7 cm • The perimeter of the trapezium is 18cm Which statements are true? Check

  17. Back Similar Question Statements 1 & 3 are true Statement 2 is false. You need to use Pythagoras’ Theorem to find the length of BC. Did you get it right? Home

  18. B ABCD is a rhombus Diagonal AC = 12cm Diagonal DB = 16cm Angle BAC = 55o A 55o E C D • Statements • Angle ABC = 70o • Perimeter of the rhombus = 40 cm • Area of rhombus = 96cm2 Which statements are true? Check

  19. Back All 3 statements are true. The diagonals of a rhombus bisect each other at right angles so you can use Pythagoras’ Theorem to calculate the length of a side. Home

  20. Algebra Foundation Higher

  21. Add two touching bricks to obtain the expression in the brick above them. 100 ? 13x 7x 6x x • Statements • 7x + 6x = 13x • 6x + x = 7x • The value of x must be 5 Check Which statements are true?

  22. Back Similar Question All 3 statements are true 20x = 100 x = 5 Home

  23. Add two touching bricks to obtain the expression in the brick above them. 60 4x + 2 ? 3x + 7 x - 5 5x + 3 • Statements • (3x + 7) + (x – 5) = 4x + 2 • (x – 5) + (5x + 3) = 6x + 2 • The value of x must be 6 Check Which statements are true?

  24. Back Statements 1 & 3 are true. Statement 2 is not true because (x – 5) + (5x + 3) = 6x - 2 Was it easy? Home

  25. This is a 12m by 10m rectangular garden. On two sides is a path of x metres width. The remaining two thirds of the garden is grass. x m 10 m x m 12m • Statements • x < 10 • x 2 - 22x + 40 = 0 • The width of the path is 2 cm Check Which statements are true?

  26. Back Similar Question Statements 1 & 2 are true. Statement 3 is not true because the width is 2 metres (not cm) Did you get it right? Home

  27. This is a 12m by 10m rectangular garden. A path of width ymetres surrounds a lawn at the centre of the garden. 12m The area of the path is twice the area of the lawn. 8 m y m • Statements • The area of the path is 64 cm2 • The area of the path is 44y cm2 • y < 2 y m Check Which statements are true?

  28. Back Only statement 1 is true. The area of the path is 8y 2 – 80y + 192 so y = 2 Home

  29. Triangles Foundation Higher

  30. ABC is a right angled triangle A • Statements • You can use Pythagoras’ Theorem to find AC • AC2 = 152 + 82 • AC =289 m 15 m B C 8 m Check Which statements are true?

  31. Back Similar Question Statements 1 & 2 are true. Statement 3 is false. AC2 = 289 AC = √289 = 17 m Home

  32. A 13-foot ladder leans against a 12-foot wall so that the top of the ladder just reaches the top of the wall. A bottom of the ladder is x feet from the base of the wall. 12 feet 13 feet • Statements • You can use Pythagoras’ Theorem to find x. • x2 = 122 + 132 • The value of x is 5 x feet Check Which statements are true?

  33. Back Statements 1 & 3 are true. Statement 2 is false. The correct equation is 132 = 122 + x 2 Choose a new starter Home

  34. A 13-foot ladder leans against a 12-foot wall so that the top of the ladder just reaches the top of the wall. A ladder makes an angle of Θ with the ground. 12 feet 13 feet • Statements • Tan Θ = 12/13 • Tan Θ = 2.4 • The value of Θ is 67.3o to 1 decimal place Θ Check Which statements are true?

  35. Back Similar Question Only statement 2 is true. Statement 1 is false because Sin Θ = 12/13 Statement 3 is false because Θ is 67.4o to 1 d.p. Home

  36. A wheel chair ramp rises by 75 cm. The angle of the ramp is 12o. The length of the ramp is x metres. 75cm 12o x m • Statements • tan 12o = 75/x • 75cm = 7.5 m • x = 3.53 to 3 s.f. Check Which statements are true?

  37. Back Only statement 3 is true. 75 cm = 0.75 m So tan 12o = 0.75/x Home

  38. Statistics Foundation Higher

  39. This table shows the ages of children in a club. • Statements • The mode is 7 years • The median is 9 years • The mean is 45 ÷ 21 Check Which statements are true?

  40. Back Similar Question None are true The mode is the most common age = 10 years The median is the middle age in order (11th out of 21) Median = 10 years. Sum of the ages = 14 + 24 + 36 + 70 + 55 So the mean is 199 ÷ 21 = 9.48 Home

  41. This table shows the ages of people in a village. • Statements • The ages of 25 people are recorded • The modal class is 20 < x ≤ 40 • The best estimate for the median is 50 Check Which statements are true?

  42. Back Statements 1 & 2 are true. Statement 3 is not true. The median value is the first of the 4 values in the 40 < x ≤ 60 interval. So 45 is a better estimate. Home

  43. This table shows the number of books read by a class of pupils during a Charity Readathon • Statements • Altogether there were 30 pupils • Altogether, they read 35 books • Mean = 6 books Check Which statements are true?

  44. Back Similar Question Statements 1 & 3 are true. Statement 2 is not true. The pupils read 180 books altogether Try another Home

  45. This table shows the ages of people who live in a village. • Statements • A good estimate for the mean is 45 years • The most densely populated class is 20 < x ≤ 40 • On a histogram the relative frequency for the interval 60 < x ≤ 70 would be 0.6 Which statements are true? Check

  46. Back Statements 1 & 3 are true. Statement 2 is not true. 20 < x ≤ 40 is the most populated but not the most densely populated (relative frequency is 0.45) Home

  47. Probability Foundation Higher

  48. Each day the school bus passes a set of traffic lights. The probability the lights are red is 0.35 The probability the lights are amber is 0.1 • Statements • Probability that the lights are red or amber = 0.36 • Probability that they are green = 0.55 • Probability that they are not red = 0.75 Which statements are true? Check

  49. Back Similar Question Statements 1 is not true ( 0.35 + 0.1 = 0.45) Statement 2 is true prob(green) = 1 – 0.45 Statement 3 is not true. prob (not red) = 1 – prob (red) = 0.65 Home

  50. A ball is picked at random from each bag Bag A Bag B • Statements • The probability of picking a blue ball from bag A is 0.3 • You are more likely to pick a bluefrom bag B than bag A • You are more likely to pick green from bag A than bag B Check Which statements are true?

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