Sub-topic 1
2025 · National One-Eighth
Free
Does a triangle centre lie inside the triangle? centroid, circumcentre, orthocentre and incentre (true/false)
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Sub-topic 2
2026 · National One-Eighth
Premium
Vacuous truth: if the angle sum is $200^\circ$ then the triangle is a square (true/false)
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Sub-topic 3
2026 · National Preliminary
Premium
Exterior angles of a triangle with interior angles in the ratio $2:3:5$
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Sub-topic 4
2025 · National Preliminary
Premium
Smallest and largest angles of a triangle in the ratio $2:3:5$
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Sub-topic 5
2026 · National Semifinal
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Area of a triangle with sides $\sqrt{7}$, $2\sqrt{5}$ and $3\sqrt{3}$
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Sub-topic 6
2026 · National Quarterfinal
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Area of a triangle with sides $\sqrt{7}$, $2\sqrt{7}$ and $\sqrt{35}$
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Sub-topic 7
2026 · National One-Eighth
Premium
Riddles: the circumcentre, centroid, orthocentre and incentre
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Sub-topic 8
2026 · National Preliminary
Premium
Which sides and angles determine a triangle, such as ssa and sas (true/false)
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Sub-topic 9
2026 · National Preliminary
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Angles $x+30$, $x-20$ and $2x-30$ of a triangle
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Sub-topic 10
2012 · National Preliminary
Premium
Triangle $abc$ where $b=2a$ and $c=a+20^\circ$
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Sub-topic 11
2012 · National Preliminary
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Triangle $abc$ where $a=2b$ and $b=3c$
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Sub-topic 12
2012 · National Preliminary
Premium
A triangle has at most one obtuse angle (true/false)
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Sub-topic 13
2013 · National Preliminary
Premium
Riddles: similarity and congruence
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Sub-topic 14
2013 · National Preliminary
Premium
Similar figures are not necessarily congruent (true/false)
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Sub-topic 15
2013 · National Preliminary
Premium
The longer side of a triangle is opposite the greater angle (true/false)
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Sub-topic 16
2013 · National Quarterfinal
Premium
Opposite angles of a kite (true/false)
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Sub-topic 17
2013 · National Quarterfinal
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Opposite and adjacent angles of a rhombus (true/false)
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Sub-topic 18
2013 · National Quarterfinal
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Corresponding angles cut by a transversal (true/false)
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Sub-topic 19
2013 · National Quarterfinal
Premium
Alternate interior angles are congruent, not complementary (true/false)
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Sub-topic 20
2016 · National Preliminary
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Complementary angles can be congruent, $45^\circ$ each (true/false)
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Sub-topic 21
2016 · National Preliminary
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Any two right angles are congruent (true/false)
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Sub-topic 22
2016 · National Preliminary
Premium
A parallelogram with congruent diagonals is a rectangle (true/false)
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Sub-topic 23
2016 · National Preliminary
Premium
A rhombus with congruent diagonals is a square (true/false)
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Sub-topic 24
2018 · National Preliminary
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The diagonals of a rectangle form two pairs of congruent triangles (true/false)
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Sub-topic 25
2020 · National One-Eighth
Premium
Diagonals of a rhombus are perpendicular but not congruent (true/false)
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Sub-topic 26
2020 · National One-Eighth
Premium
Diagonals of a rectangle are congruent but not perpendicular (true/false)
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Sub-topic 27
2021 · National Quarterfinal
Premium
Right-angled triangle with sides $x$, $2x-1$ and $2x+1$
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Sub-topic 28
2021 · National Quarterfinal
Premium
Riddles: quadrilaterals such as the isosceles trapezium, kite and rhombus
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Sub-topic 29
2022 · National Preliminary
Premium
Angles when one angle is twice another and the third is $40^\circ$ more than the smallest
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Sub-topic 30
2022 · National Preliminary
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Angles when one angle is thrice another and the third is $45^\circ$ more than the smallest
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Sub-topic 31
2022 · National Preliminary
Premium
Angles when two are congruent and the third is $30^\circ$ more
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Sub-topic 32
2022 · National Preliminary
Premium
Riddles: vertically opposite, corresponding and alternate angles
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Sub-topic 33
2022 · National One-Eighth
Premium
An "auto center" is not a triangle centre (true/false)
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Sub-topic 34
2023 · National One-Eighth
Premium
Legs of a right triangle with a $1:2$ leg ratio and hypotenuse $10$ cm
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