6.2 Understand and construct geometrical proofs using formal arguments Quiz: AQA Further Maths, Unit 6

The 20 questions

1. What term describes a logical chain of reasoning used to show a mathematical statement is true?

   • Estimate
   • Proof
   • Conjecture
   • Measurement

2. What must accompany each step in a formal geometrical proof to justify it?

   • A diagram
   • A measurement
   • A calculation
   • A reason

3. Which theorem shows that base angles of an isosceles triangle are equal?

   • Alternate angles
   • Isosceles triangle theorem
   • Pythagoras' theorem
   • Sine rule

4. What do the angles at a point add up to?

   • 180 degrees
   • 90 degrees
   • 270 degrees
   • 360 degrees

5. A triangle is inscribed in a circle with one side as a diameter. What is the angle opposite that diameter?

   • 45 degrees
   • 90 degrees
   • 60 degrees
   • 180 degrees

6. What must be stated at the very end of a completed geometrical proof?

   • The conclusion
   • A counterexample
   • A measurement
   • An assumption

7. For alternate angles to be equal in a geometrical proof, what condition must the lines meet?

   • Perpendicular lines
   • Equal length lines
   • Intersecting lines
   • Parallel lines

8. Why is showing that a rule works for three specific triangles not a valid proof?

   • Invalid shapes
   • Incorrect calculations
   • Incomplete cases
   • Missing measurements

9. Which angle property is key when proving that the interior angles of a triangle total 180°?

   • Alternate angles
   • Opposite angles
   • Interior angles
   • Reflex angles

10. Which type of triangle pair is used to prove that tangents from an external point are equal?

    • Similar isosceles
    • Congruent right-angled
    • Congruent isosceles
    • Similar right-angled

11. What effect does a line drawn perpendicular from the centre of a circle to a chord have?

    • It trisects it
    • It bisects it
    • It parallels it
    • It doubles it

12. Logical reasoning where conclusions follow necessarily from established geometric facts is called what?

    • Empirical reasoning
    • Circular reasoning
    • Deductive reasoning
    • Inductive reasoning

13. Why must every step in a formal geometrical proof include an explicit mathematical reason?

    • To show working
    • To justify statements
    • To simplify calculations
    • To define variables

14. Which statement represents a valid reason when constructing a formal geometric proof?

    • Opposite angles equal
    • Sides seem equal
    • Angles look equal
    • Lines look parallel

15. The exterior angle of any triangle is equal to the sum of which angles?

    • Two opposite exterior
    • Two adjacent interior
    • All three interior
    • Two opposite interior

16. In any cyclic quadrilateral, which pair of angles always adds up to 180°?

    • Adjacent angles
    • Opposite angles
    • Corresponding angles
    • Alternate angles

17. Which congruence condition uses two sides and the included angle?

    • SSS
    • RHS
    • SAS
    • ASA

18. How many triangles are needed to prove the angles of a quadrilateral sum to 360 degrees?

    • 1
    • 4
    • 3
    • 2

19. Besides a right angle and hypotenuse, what else must match for RHS congruence?

    • One other side
    • The triangle area
    • Both non-right angles
    • One non-right angle

20. Which reason proves that all interior angles in an equilateral triangle are 60°?

    • Pythagoras theorem
    • 180° divided equally
    • Exterior angle rule
    • Symmetry across axes

Related quizzes

• Knowledge of perimeter, area and volume of 2D and 3D shapes (title taken from Notes column; Content cell blank) Quiz · 6.1 · 20 questions
• Sine and cosine rules in scalene triangles; area of a triangle = ab sinC Quiz · 6.3 · 20 questions
• Use of Pythagoras’ theorem in 2D and 3D Quiz · 6.4 · 20 questions
• Be able to apply trigonometry and Pythagoras’ theorem to 2 and 3 dimensional problems Quiz · 6.5 · 20 questions
• Sketch and use graphs of y = sin x, y = cos x and y = tan x for angles of any size Quiz · 6.6 · 20 questions
• Be able to use the definitions sin θ, cos θ and tan θ, for any positive angle up to 360°(measured in degrees only) Quiz · 6.7 · 20 questions
• Knowledge and use of 30°, 60°, 90° triangles and 45°, 45°, 90° triangles Quiz · 6.8 · 20 questions
• Know and use tan θ = sin θ / cos θ and sin2θ + cos2θ = 1 Quiz · 6.9 · 20 questions
• Solution of simple trigonometric equations in given intervals Quiz · 6.10 · 20 questions
• Knowledge and use of numbers and the number system including fractions, decimals, percentages, ratio, proportion and order of operations Quiz · 1.1 · 20 questions