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Q1. How many altitudes can a triangle have?

• 3
• 2
• 1
• 0

Solution

Altitude is a perpendicular drawn from the vertex of a triangle to the side opposite to it. Each triangle has three vertices hence it has three altitudes.

Q2. The exterior angle of a triangle is 80⁰. If one of the interior opposite angles is 35⁰, the measure of the other two angles is

• 100⁰; 45⁰
• 50⁰; 50⁰
• 40⁰; 60⁰
• 80⁰; 20⁰

Solution

In the figure, a + 80⁰ = 180⁰     ......(linear pair) Thus, a = 100⁰ b + 35⁰ = 80⁰      ........(Since exterior angle = sum of interior opposite angles) Thus, b = 45⁰

Q3. Which of the following can be the sides of a right angled triangle?

• 8, 10, 5
• 8, 17, 15
• 7, 8, 9
• 1, 3, 6

Solution

We have 17² = 289 and 8² + 15² = 64 + 225 = 289 This give 17² = 8² + 15² Therefore, 8, 17, 15 are the sides of a right angled triangle.

Q4. If two sides of a triangle are 4 cm and 5 cm then which of the following cannot be the length of third side?

• 7 cm
• 6 cm
• 10 cm
• 8 cm

Solution

The sum of two given sides is 4 cm + 5 cm = 9 cm Hence, 10 cm cannot be the length of third side as the sum two sides is always greater than third side.

Q5. For a triangle ABC, which of the following is true?

• AB + BC > AC
• AB + BC < AC
• AB + BC = AC
• AB + BC > or = AC

Solution

For any triangle, sum of two sides is always greater than the third side.

Q6. In a triangle ABC, if AP is a median, then which of the following is true?

• AP = PB
• BP = CP
• AP = PC
• AB = AC

Solution

Since the median is drawn from the vertex A, therefore it divides the side BC in two equal parts.

Q7. If a side of a triangle is produced, the exterior angle so formed is equal to the

• Sum of adjacent angles of the triangle
• Sum of interior opposite angles of the triangle
• Sum of exterior angles
• Sum of exterior opposite angles

Solution

Exterior angle of a triangle is equal to the sum of interior opposite angles of the triangle.

Q8. In an isosceles triangle, if the vertex angle is twice the sum of the equal base angles, then the angles of the triangle are

• 120^o, 30^o, 30^o
• 60^o, 60^o, 60^o
• 80^o, 50^o, 50^o
• 90^o, 45^o, 45^o

Solution

Let the base angles be x and x. Then, vertical angle = 4x. Now, x + x + 4x = 180^o                       (angle sum property of a triangle)  x = 30^o Hence, angles of the triangle are 120^o, 30^o, 30^o.

Q9. In a triangle PQR, PQ = 2 cm, QR = 3 cm and RP = 4 cm. The angle with larger measure is:

• Angle P
• Angle Q
• Angle R
• None

Solution

Larger side = RP = 4 cm Thus, the angle with larger measure is Angle Q as it is opposite to the largest side RP.

Q10. Sum of an exterior angle of a triangle and adjacent interior angle is __________.

• 180⁰
• 360⁰
• 90⁰
• 240⁰

Solution

180⁰ as they form a linear pair.

Q11. How many altitudes can a right angled triangle have?

• 2
• 1
• 4
• 3

Solution

Every triangle can have 3 altitudes.

Q12. Which of the following angles form a triangle?

• 100o, 50o, 40o
• 110o, 50o, 40o
• 10o, 70o, 40o
• 160o, 10o, 10o

Solution

The angle sum property of a triangle states that the sum of all angles of a triangle is equal to 180°.  Since 160o+10o+ 10o= 180o The angles 160°, 10° and 10° make a triangle. 

Q13. In a right angled triangle, if the length of sides are 3 cm and 4 cm, then the length of hypotenuse is

• 2 cm
• 4 cm
• 5 cm
• 6 cm

Solution

For a right angled triangle, (Hypotenuse)² = 3² + 4² = 9 + 16 = 25 Thus, Hypotenuse = 5 cm

Q14. In a triangle if all angles are equal then

• All sides are also equal
• All sides are may or may not equal
• All sides cannot be equal
• Any two sides are equal

Solution

All sides are equal.

Q15. Which of the following are the sides of right angled triangle?

• 8, 6, 11
• 8, 7, 10
• 7, 6, 10
• 8, 6, 10

Solution

As (8)² + (6)² = (10)² By Pythagoras property, 8, 6, 10 are the sides of right angled triangle.

Q16. In an isosceles triangle ABC, AB = AC and angle A measures 70⁰, then the measure of angle B is:

• 55^o
• 45^o
• 35^o
• 60^o

Solution

In isosceles triangle ABC, AB = AC Thus, Angle B = Angle C Now, Angle A + Angle B + Angle C = 180⁰ 70⁰ + 2(Angle B) = 180⁰ 2(Angle B) = 180⁰ - 70⁰ So, Angle B =

Q17. Which of the following is a Pythagorean triple?

• 3, 4, 5
• 3, 4, 6
• 2, 4, 5
• 1, 2, 3

Solution

As, (3)² + (4)² = (5)² By pythagoras property, 3, 4, 5 are the sides of right angled triangle.

Q18. The medians of _____________ triangle are equal in length.

• an Isosceles
• a scalene
• an equilateral
• a Right angled

Solution

an equilateral

Q19. In which of the following triangle corresponding altitudes and medians coincides?      

• Scalene triangle
• Isosceles triangle
• Equilateral triangle
• Obtuse angle triangle

Solution

In case of equilateral triangle corresponding altitudes and medians coincides.

Q20. An exterior angle of a triangle is 110^o; and one of the interior opposite angles is 30^o, then the other two angles of the triangle are

• 60^o, 70^o
• 120^o, 80^o
• 70^o,  80^o
• 50^o,   60^o

Solution

Exterior angle of a triangle is equal to the sum of interior opposite angles of the triangle. Hence, 30^o + other interior angle = 110^o \ other interior angle = 80^o By the angle sum property of a triangle 30^o + 80^o + third angle = 180^o \ Third angle = 70^o

Q21. A line joining the vertex of a triangle to the mid point of side opposite to it is called

• Median
• Altitude
• Angle Bisector
• Side

Solution

By the definition, A line joining the vertex of a triangle to the mid point of its opposite side  is called the median.

Q22. PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

• 44 cm
• 14 cm
• 25 cm
• 26 cm

Solution

Q23. The side opposite to acute angles of a right angled triangle are 7 cm and 24 cm, the side opposite to right angle is

• 25 cm
• 28 cm
• 22 cm
• 26 cm

Solution

Q24. If all three angles of a triangle are equal then the measure of each angle is    

• 50o
• 40o
• 70o
• 60o

Solution

Let the measure of each angle be x. Then, x + x + x = 180^o   3x = 180^o x =

Q25. Which of the following will be the measure of exterior angle of an equilateral triangle?

• 120^o
• 60^o
• 180^o
• 150^o

Solution

Measure of each angle of an equilateral triangle is 60^o. Exterior angle = 180^o - 60^o = 120^o

Q26. State which of the following statement is true.

• Altitudes and medians of an equilateral triangle are same.
• Altitudes and medians of an equilateral triangle are not same.
• Altitudes and medians of an isosceles triangle are same.
• Altitudes and medians of an isosceles triangle are not same.

Solution

Only option A is correct.

Q27. Sum of all the exterior angles formed by producing the sides of the triangle is

• 180⁰
• 150⁰
• 540⁰
• 360⁰

Solution

Since a + b + c = 180^o

Q28. Which of the following sides can give a valid triangle?

• 2 cm, 3 cm, 7 cm
• 2 cm, 10 cm, 7 cm
• 12 cm, 3 cm, 7 cm
• 5 cm, 3 cm, 7 cm

Solution

For sides given in option D, sum of any two sides is always greater than third side, so it will give a valid triangle.

Q29. In a right angled triangle, if the length of sides are 12 cm and 5 cm, then the length of hypotenuse is

• 13 cm
• 16 cm
• 14 cm
• 17 cm

Solution

For a right angled triangle, (Hypotenuse)² = 5² + 12² = 25+ 144 = 169 Thus, Hypotenuse = 13 cm

Q30. Which of the following sides form a triangle?

• 7.2 cm, 4.1 cm, 2.5 cm
• 10.5 cm, 4.5 cm, 4.5 cm
• 7.2 cm, 4.1 cm, 3.5 cm
• 5.2 cm, 1.1 cm, 2.5 cm

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