CBSE Class 7 Mathematics Triangles and Its Properties Assignment Set A

Question. In a ΔABC, if AB² = BC² + AC², at which vertex is the right angle?
(A) A
(C) c
(B) B
(D) Either A or B
Answer : C

Question. Which type of triangle is formed by BC = 7.2 em, AC = 6 em and ∠c = 120° ?
(A) An acute angled triangle.
(B) An obtuse angled triangle .
(C) A right angled triangle.
(D) An isosceles triangle.
Answer : B

Question. Which triangle is formed by AB = 3 em, BC = 4 em and AC = 8 em?
(A) A scalene triangle.
(B) An isosceles triangle.
(C) An equilateral triangle.
(D) No triangle is formed.
Answer : D

Question. If two angles in a triangle are 65° and 85°, what is the third angle?
(A) 30°
(B) 45°
(C) 60°
(D) 90°
Answer : A

Question. If one angle is the average of the other two angles and the difference between the greatest and least angles is 60°, which triangle is formed?
(A) An isosceles triangle.
(B) An equilateral triangle.
(C) A right angled triangle.
(D) A right angled isosceles triangle.
Answer : C

Question. In ΔABC, if AB = BC and ∠B = 80°, what is the measure of ∠C ?
(A) 50°
(C) 130°
(B) 100°
(D) 180°
Answer : A

Question. Which triangle is formed by BC = AC = 7.2 em and ∠C = 90°?
(A) A right angled triangle.
(B) An isosceles triangle.
(C) A right angled isosceles triangle.
(D) No triangle is formed.
Answer : C

Question. Which of the following statements is false?
(A) The sum of two sides of a triangle is greater than the third side.
(B) In a right angled triangle, hypotenuse is the longest side .
(C) A, B and C are collinear if AB+ BC =AC.
(D) The sum of angles in a triangle is less than 180°.
Answer : D

Question. What is the length of the hypotenuse of a right angled triangle whose two legs measure 12 em and 0.35 m?
(A) 37 em
(B) 3.72 em
(C) 0.372 em
(D) 37 m
Answer : A

Question. If the two legs of a right angled triangle are equal and the square of the hypotenuse is 100 sq units, what is the length of each leg?
(A) 10 units
(B) 5√2 units
(C) 10√J2 units
(D) 15 units
Answer : B

Question. In a ΔPQR. PQ = PR and ∠Q is twice that of ∠P . What is the measure of ∠Q ?
(A) 72°
(B) 36°
(C) 144°
(D) 108°
Answer : A

Question. If two sides of an isosceles triangle are 3 em and 8 em, what is the length of the third side?
(A) 3 em
(B) 8 em
(C) 3 em or 8 em
(D) Neither (A) nor (B)
Answer : B

Question. If in a ΔABC, ∠A = 60° and AB = AC, of what type is ΔABC?
(A) An isosceles triangle.
(B) A right angled triangle.
(C) An isosceles right angled triangle .
(D) An equilateral triangle.
Answer : D

Question. In a ΔABC, if AB + BC = 10 em, BC + CA = 12 em, CA + AB = 16 em, what is the sum of the lengths of its sides?
(A) 1g em
(B) 17 em
(C) 38 em
(D) 30 em
Answer : A

Question. Which of the following are the angles in a right angl ed triangle other than the right angle?
(A) Acute angles
(B) Obtuse angles
(C) Right angles
(D) Reflex angles
Answer : A

Question. In a ΔABC, if ∠A = ∠B + ∠C , what is the measure of ∠A
(A) 60°
(B) 45°
(C) 900
(D) 135°
Answer : C

Question. If a, b and c are the sides of a triangle, which of the following is correct?
(A) a - b > c
(B) c > a + b
(C) c = a + b
(D) b < c + a
Answer : D

Question. If the angles of a triangle are in the ratio 1 : 2: 7, what type of a triangle is it?
(A) An acute angled triangle.
(B) An obtuse angled triangle.
(C) A right angled triangle.
(D) A right angled isosceles triangle.
Answer : B

Question. A triangle always has
(A) exactly one acute angle.
(B) exactly two acute angles.
(C) at least two acute angles.
(D) exactly 2 right angles.
Answer : C

Question. How many independent measurements are required to construct a triangle?
(A) 3
(B) 4
(C) 2
(D) 5
Answer : A

Question. In a ΔABC, if ∠B is an obtuse angle, which is the longest side?
(A) AB
(C) AC
(B) BC
(D) Either (A) or (B)
Answer : C

Question. If P : An isosceles triangle is right angled.
Q: ∠A = ∠B = 45° and ∠C = 90°, which of the following statements is true?
(A) P is true and Q is the correct explanation of P.
(B) P is true and Q is not the correct explanation of P.
(C) P is false.
(D) P is the correct explanation of Q.
Answer : A

Question. An isosceles triangle can be obtuse angled.
(A) Always false.
(B) Always true.
(C) Cannot be determined.
(D) Sometimes false.
Answer : D

Question. Which of the following statements is correct?
(A) The difference of any two sides is less than the third side.
(B) A triangle cannot have two obtuse angles.
(C) A triangle cannot have an obtuse angl e and a right angle.
(D) All the above
.Answer : D

Question. Two chimneys 18m and 13m high stand upright on a ground. If their feet are 12m apart, what is the distance between their tops?
(A) 5 m
(B) 31 m
(C) 13 m
(D) 18 m
Answer : C

Question. The top of a broken tree touches the ground at a distance of 15 m from its base.
If the tree is broken at a height of 8 m from the ground, what is the actual height of the tree?
(A) 20 m
(B) 25 m
(C) 30 m
(D) 17 m
Answer : B

Question. What is the ratio in which the centroid of a triangle divides the medians ?
(A) 1 : 2
(B) 1 : 3
(C) 2: 1
(D) 3 : 1
Answer : C

Question. The centroid of a triangle is the point of concurrence of which of these?
(A) Angle bisectors
(B) Perpendicular bisectors
(C) Altitudes
(D) Medians
Answer : D

Question. Which of the following statements is true?
(A) The centroid of an acute angled triangle lies in the interior of the triangle.
(B) The orthocentre of an acute angled triangle lies in the interior of the triangle.
(C) The medians of a triangle are concurrent.
(D) All the above
Answer : D

Question. In ΔABC, Dis the midpoint of BC and G is the centroid of the triangle. If GO = 2 em, what is the length of AD ?
(A) 4 em
(B) 6 em
(C) 2 em
(D) 8 em
Answer : B

Question. In a ΔABC, E is the midpoint of AC and G is the centroid of the triangle. What is BE: GE?
(A) 1 : 2
(B) 2 : 1
(C) 3 : 1
(D) 1 : 3
Answer : C

Question. Which of the following statements is true?
(A) The orthocentre of a right angled triangle is the vertex containing the right angle.
(B) The median of a triangle joins a vertex to the midpoint of the opposite side.
(C) The centroid of a right angled triangle lies in the interior of the triangle.
(D) All the above.
Answer : D

Question. In a scalene triangle ABC, X is the midpoint of BC. What is AX?
(A) Median
(B) Altitude
(C) Centroid
(D) Orthocentre
Answer : A

Question. In ΔPQR, PQ = PR ; M is a point on QR and PM ⊥ QR . What do you call PM?
(A) Centroid
(B) Median
(C) Altitude
(D) Vertex
Answer : C

Question. In ΔXVZ, XP is the median.Which of the following is correct?
(A) XP = XV
(B) VP = PZ
(C) XP = XZ
(D) XV= XZ
Answer : B

Question. From the figure given, which of the following statements is true ?
(A) ∠x + ∠y = ∠1 + ∠3
(B) ∠y = ∠2
(C) ∠x = ∠1
(D) ∠x + ∠y = ∠1 + ∠2
Answer : D

Question. The exterior angle of a triangle is 110". If one of the interior opposite angles is 55", what is the measure of the other ?
(A) 45"
(B) 65"
(C) 55"
(D) 35"
Answer : C

Question. In ΔPQR, ∠Q = 90" Which of the following is the longest side?
(A) RQ
(B) PQ
(C) PR
(D) Either (A) or (B)
Answer : C

Question. Which of the following statements is NOT true?
(A) A triangle can have three 60° angles.
(B) A triangle can have a right angle.
(C) A triangle can have two right angles.
(D) A triangle can have all three angles equal.
Answer : C

Question. From the following figure, what are the respective values of x and y?
(A) 80°, 60°
(C) 60°, 80°
(B) 60°, 40°
(D) 40°, 60°
Answer : A

Q1.Fill in the blanks:

a) A __________________ of a triangle connects one of its vertex to the midpoint of the opposite side.

b) A triangle can have ______ altitudes.

c) A triangle can have _____________ medians.

d) In a _____________ triangle two of its sides are its altitudes.

e) In an ____________ triangle, the median and altitude are given by the same line segment.

f) ___________________ is the longest side in a right triangle.

g) By Pythagoras theorem (___________)² = (______)² + (_______)²

Q2. State:

a) Angle sum property of a triangle.

b) Pythagoras property

c) Property of the lengths of sides of a triangle.

Q3. Find the value of x:

Q4. The lengths of two sides of a triangle are 12cm and 15cm. Between what two measures should the length of the third side fall?

Q5. ABCD is a quadrilateral. Is AB + BC + CD + DA < 2(AC + BD) ?

Q6. Determine whether the triangle whose lengths of sides are 4, 5, 6 is a right angled triangle.

Q7. ΔABC is right angled at C. If AC=5cm and BC=12cm, find the length of AB.

Q8. Is there a triangle whose sides have length 10.2cm, 5.8cm and 4.5cm?

Q9. Find the values of the unknowns x and y in the following figures

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