Construction of Triangles: 18 MCQs

All 18 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 30 Quick Revision · 15

Warm-up · 7 questions

Q1. Three points are said to be non-collinear when:

Beginner

A They form a right angle at one point.

B They all lie on the same straight line.

C They do not all lie on the same straight line.

D They are all at the same distance from a fixed point.

Answers and explanations are in the Veda app.

Q2. In ∆ABC, which side is opposite vertex A?

Beginner

A AC

B BC

C AB

D CA

Answers and explanations are in the Veda app.

Q3. A triangle has how many elements in total?

Beginner

A Four

B Three

C Six

D Nine

Answers and explanations are in the Veda app.

Q4. To construct an equilateral triangle of side 5 cm, you draw two circles. What radius should each circle have?

Beginner

A The radius can be any length.

B 5 cm

C 2.5 cm

D 10 cm

Answers and explanations are in the Veda app.

Q5. An altitude of a triangle is:

Beginner

A The longest side of the triangle.

B The perpendicular from a vertex to the line containing the opposite side.

C A line that bisects an angle of the triangle.

D A line joining a vertex to the midpoint of the opposite side.

Answers and explanations are in the Veda app.

Q6. The three altitudes of a triangle are concurrent. Their point of concurrence is called the:

Beginner

A Centroid

B Circumcentre

C Orthocentre

D Incentre

Answers and explanations are in the Veda app.

Q7. The sum of the three angles of any triangle is always 180°.

Beginner

A True

B False

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Building up · 6 questions

Q8. Which of these sets of sides CANNOT form a triangle?

Intermediate

A 2 cm, 3 cm, 6 cm

B 4.8 cm, 6.2 cm, 10.5 cm

C 4 cm, 5 cm, 6 cm

D 6 cm, 8 cm, 10 cm

Answers and explanations are in the Veda app.

Q9. If two sides of a triangle are 6 cm and 8 cm, the third side must lie strictly between:

Intermediate

A 0 cm and 14 cm

B 2 cm and 14 cm

C 6 cm and 8 cm

D 2 cm and 8 cm

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Q10. A triangle has angles 42°, 17° and one unknown angle. What is the unknown angle?

Intermediate

A 59°

B 180°

C 121°

D 138°

Answers and explanations are in the Veda app.

Q11. In a right-angled triangle, the two acute angles are:

Intermediate

A Both obtuse

B Complementary

C Equal to each other

D Supplementary

Answers and explanations are in the Veda app.

Q12. A triangle has sides 3 cm, 3 cm and 3 cm. Which description applies?

Intermediate

A Equilateral and acute-angled

B Scalene and obtuse-angled

C Isosceles and obtuse-angled

D Isosceles and right-angled

Answers and explanations are in the Veda app.

Q13. Which set of angles CANNOT be the three angles of a triangle?

Intermediate

A 30°, 60°, 90°

B 50°, 60°, 70°

C 100°, 90°, 10°

D 45°, 45°, 90°

Answers and explanations are in the Veda app.

Topper level · 5 questions

Q14. In an obtuse-angled triangle, what must be done before dropping an altitude from the vertex opposite an obtuse angle's adjacent side?

Advanced

A The altitude must be drawn inside the triangle.

B The side must be extended so the perpendicular can meet it.

C The obtuse angle must be bisected first.

D The triangle must be redrawn as acute.

Answers and explanations are in the Veda app.

Q15. A student constructs a triangle with sides 4 cm, 5 cm and 6 cm by drawing a 6 cm circle from A and a 5 cm circle from B on AB = 4 cm. What is wrong?

Advanced

A The circles should both have radius 4 cm.

B The base AB should be 5 cm, not 4 cm.

C The radii are swapped: the 5 cm circle should be from A and the 6 cm circle from B.

D Only one circle is needed for this construction.

Answers and explanations are in the Veda app.

Q16. A triangle has one angle of 95°. Which statement must be true?

Advanced

A The other two angles must both be greater than 45°.

B The triangle is right-angled.

C The triangle is obtuse-angled and the other two angles are acute.

D The triangle is acute-angled.

Answers and explanations are in the Veda app.

Q17. Given the sides of a triangle are 4 cm, 5 cm, and 6 cm, which of the following statements about constructing this triangle is correct?

Advanced

A Draw a circle of radius 6 cm from vertex A and 5 cm from vertex B.

B Draw a circle of radius 4 cm from vertex B and 5 cm from vertex A.

C Draw a circle of radius 4 cm from vertex A and 5 cm from vertex B.

D Draw a circle of radius 5 cm from vertex A and 6 cm from vertex B.

Answers and explanations are in the Veda app.

Q18. If two sides of a triangle are 6 cm and 8 cm, what is the range of possible lengths for the third side?

Advanced

A The third side must be exactly 7 cm.

B The third side must be between 2 cm and 14 cm.

C The third side must be between 4 cm and 10 cm.

D The third side must be between 1 cm and 15 cm.

Answers and explanations are in the Veda app.

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