A Tale of Three Intersecting Lines — Quiz

Q1. Ravi names a triangle as ΔABC while Priya names the same triangle as ΔBCA. Which statement is correct?

• A. Only Ravi's name is valid; the vertices must be written in alphabetical order
• B. Both names are wrong; a triangle should be named using a single letter
• C. Only Priya's name is valid; the vertex with the largest angle must come first
• D. Both names are valid because the vertices of a triangle may be written in any order

Q2. Suppose three points A, B and C lie on a single straight line. What happens if we try to form a triangle ΔABC?

• A. A right-angled triangle is formed
• B. An equilateral triangle is formed
• C. An obtuse-angled triangle is formed
• D. No triangle is formed, as the three segments fall on the same line

Q3. While constructing an equilateral triangle on base AB = 4 cm, the third vertex C is taken as the intersection of two 4 cm arcs from A and B. Why does this give AC = BC = 4 cm?

• A. Because the compass automatically draws equal sides
• B. Because the arcs always meet at a point exactly above the midpoint of AB
• C. Because any point above AB is at 4 cm from both A and B
• D. Because C lies on both arcs, so its distance from A and from B is 4 cm each

Q4. To construct a triangle ABC with AB = 4 cm, AC = 5 cm and BC = 6 cm using a compass, after drawing AB = 4 cm the next step is to

• A. Draw an arc of radius 4 cm from A and an arc of radius 4 cm from B
• B. Draw an arc of radius 5 cm from B and an arc of radius 6 cm from A
• C. Draw a perpendicular to AB at A and mark C at a distance of 5 cm on it
• D. Draw an arc of radius 5 cm from A and an arc of radius 6 cm from B, and let C be their intersection

Q5. To decide whether three lengths can be the sides of a triangle, the quickest single check is to compare the largest length with

• A. The smallest of the three lengths
• B. The difference between the other two lengths
• C. The product of the other two lengths
• D. The sum of the other two lengths

Q6. The chapter uses a picture of a tent, a tree and a pole to show that

• A. The roundabout path via a third point is always shorter than the direct path
• B. Only paths along a circle can be shortest paths
• C. Every path between two points has the same length
• D. The direct straight-line path between two points is shorter than the roundabout path via a third point

Q7. To check if a triangle exists, two circles are drawn with the smaller two lengths as radii and the longest length as AB. The two circles will just touch each other when

• A. The sum of the two radii is less than AB
• B. The sum of the two radii is exactly equal to AB
• C. The sum of the two radii is greater than AB
• D. The two radii are equal to each other

Q8. Out of the three cases — circles touch at one point, circles do not intersect, circles intersect at two points — which case leads to the formation of a triangle?

• A. Only when the circles touch at a single point
• B. Only when the circles do not intersect at all
• C. In all three cases a triangle is always formed
• D. Only when the circles intersect each other at two points

Q9. A triangle has sides 7 cm, 7 cm and 4 cm. By the classification based on sides, this triangle is

• A. Equilateral
• B. Right-angled
• C. Scalene
• D. Isosceles

Q10. To construct ΔABC with AB = 5 cm, ∠A = 45° and AC = 4 cm, after drawing AB = 5 cm and the 45° arm at A, the next step is to

• A. Mark a point C on the second arm of ∠A such that AC = 4 cm
• B. Draw an arc of radius 4 cm from B and intersect it with AB
• C. Draw a perpendicular to AB at B and mark C 4 cm above it
• D. Bisect AB and mark C at the midpoint

Q11. A triangle can be constructed using two given angles and the included side only when the sum of the two given angles is

• A. Equal to 90°
• B. Equal to 180°
• C. Less than 180°
• D. More than 180°

Q12. Is it possible to draw a triangle in which all three angles are 70°?

• A. Yes, this gives an acute-angled triangle
• B. Yes, this gives an equilateral triangle
• C. No, because all three angles of a triangle must be different
• D. No, because 70° + 70° + 70° = 210° ≠ 180°

Q13. In ΔABC, ∠A = 50° and ∠B = 60°. Side BC is extended to D. What is the measure of the exterior angle ∠ACD?

• A. 70°
• B. 180°
• C. 120°
• D. 110°

Q14. How many altitudes can be drawn in a triangle?

• A. Exactly one
• B. Exactly two
• C. Exactly three
• D. Infinitely many

Q15. A triangle has angles 40°, 35° and 105°. By the classification based on angles, this triangle is

• A. Obtuse-angled
• B. Acute-angled
• C. Right-angled
• D. Equilateral