Construction of Triangles: 30 flashcards
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1. What condition must three points satisfy to form a triangle?
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They must be non-collinear — not all lying on the same straight line.
2. How many elements does a triangle have, and what are they?
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Six elements: three sides and three angles.
3. In ∆ABC, which side is opposite vertex A?
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Side BC is opposite vertex A.
4. In ∆ABC, which vertex is opposite side AB?
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Vertex C is opposite side AB.
5. How do you construct an equilateral triangle of side 5 cm using ruler and compass?
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Draw AB = 5 cm. Draw a 5 cm circle from A and a 5 cm circle from B. Their intersection is C. Join AC and BC.
6. How do you construct a triangle with sides 4 cm, 5 cm and 6 cm?
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Draw AB = 4 cm. Draw a 5 cm circle from A and a 6 cm circle from B. Their intersection is C. Join AC and BC.
7. What is an altitude of a triangle?
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The perpendicular drawn from a vertex to the line containing the opposite side.
8. What is the orthocentre of a triangle?
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The point where the three altitudes are concurrent.
9. In an obtuse triangle, what must you do before drawing an altitude from the opposite vertex?
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Extend the side so the perpendicular can meet it.
10. State the triangle inequality (sum form).
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The sum of the lengths of any two sides is greater than the length of the third side.
11. State the triangle inequality (difference form).
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The difference of the lengths of any two sides is less than the length of the third side.
12. Can sides 2 cm, 3 cm and 6 cm form a triangle? Why?
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No, because 2 + 3 = 5 < 6, so the sum of the two shorter sides is not greater than the longest side.
13. If two sides of a triangle are 6 cm and 8 cm, what is the range for the third side?
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2 cm < third side < 14 cm.
14. What defines an acute-angled triangle?
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All three angles are less than 90°.
15. What defines a right-angled triangle, and what are its legs and hypotenuse?
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One angle is 90°. The sides forming the right angle are legs; the side opposite the right angle is the hypotenuse.
16. What defines an obtuse-angled triangle?
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One angle is greater than 90°; the other two are acute.
17. Why can a triangle have at most one right or obtuse angle?
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Two right angles would sum to 180°, leaving nothing for the third; two obtuse angles would exceed 180° before counting the third.
18. What is an equilateral triangle, and what is each angle?
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All three sides are equal, and each angle is 60°.
19. What is an isosceles triangle?
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A triangle with two equal sides, and the angles opposite those equal sides are also equal.
20. What is a scalene triangle?
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A triangle with no two sides equal.
21. State the angle sum property of a triangle.
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∠A + ∠B + ∠C = 180° for every triangle.
22. If ∠A = 42° and ∠B = 17°, what is ∠C?
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∠C = 180° − (42° + 17°) = 121°.
23. In a right triangle, what is the relationship between the two acute angles?
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They are complementary — they add to 90°.
24. Can angles 100°, 90° and 10° form a triangle? Why?
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No, because they sum to 200°, not 180°.
25. What is the perimeter of ∆ABC?
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AB + BC + CA.
26. Why are triangles used in bridges and trusses?
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Because triangles are rigid — they cannot be deformed without changing a side length or breaking a joint.
27. What is the common mistake when constructing a triangle from three given sides?
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Swapping the radii of the circles — centring the wrong radius on the wrong endpoint.
28. How do you construct an altitude from vertex A to side BC using compass and ruler?
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With A as centre, draw an arc cutting BC at P and Q. With P and Q as centres and radius more than half PQ, draw arcs intersecting at a point. The line through A and that intersection is perpendicular to BC.
29. Can a triangle have two obtuse angles?
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No, because two obtuse angles would sum to more than 180°, leaving no valid third angle.
30. What is the difference between an altitude and a side of a triangle?
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A side joins two vertices; an altitude is a perpendicular from a vertex to the opposite side (or its extension).
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