MCQs on Class 9 Triangles
Solve the MCQs
1) In triangle ABC, if AB=BC and ∠B = 70°, ∠A will be:
a. 70°
b. 110°
c. 55°
d. 130°
Answer: c
Explanation: Given,
AB = BC
Hence, ∠A=∠C
And ∠B = 70°
By angle sum property of triangle we know:
∠A+∠B+∠C = 180°
2∠A+∠B=180°
2∠A = 180-∠B = 180-70 = 110°
∠A = 55°
2) For two triangles, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle. Then the congruency rule is:
a. SSS
b. ASA
c. SAS
d. None of the above
Answer: b
3) A triangle in which two sides are equal is called:
a. Scalene triangle
b. Equilateral triangle
c. Isosceles triangle
d. None of the above
Answer: c
4) The angles opposite to equal sides of a triangle are:
a. Equal
b. Unequal
c. supplementary angles
d. Complementary angles
Answer: a
5) If E and F are the midpoints of equal sides AB and AC of a triangle ABC. Then:
a. BF=AC
b. BF=AF
c. CE=AB
d. BF = CE
Answer: d
Explanation: AB and AC are equal sides.
AB = AC (Given)
∠A = ∠A (Common angle)
AE = AF (Halves of equal sides)
∆ ABF ≅ ∆ ACE (By SAS rule)
Hence, BF = CE (CPCT)
6) ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Then:
a. BE>CF
b. BE<CF
c. BE=CF
d. None of the above
Answer: c
Explanation:
∠A = ∠A (common arm)
∠AEB = ∠AFC (Right angles)
AB = AC (Given)
∴ ΔAEB ≅ ΔAFC
Hence, BE = CF (by CPCT)
7) If ABC and DBC are two isosceles triangles on the same base BC. Then:
a. ∠ABD = ∠ACD
b. ∠ABD > ∠ACD
c. ∠ABD < ∠ACD
d. None of the above
Answer: a
Explanation: AD = AD (Common arm)
AB = AC (Sides of isosceles triangle)
BD = CD (Sides of isosceles triangle)
So, ΔABD ≅ ΔACD.
∴ ∠ABD = ∠ACD (By CPCT)
8) If ABC is an equilateral triangle, then each angle equals to:
a. 90°
B.180°
c. 120°
d. 60°
Answer: d
Explanation: Equilateral triangle has all its sides equal and each angle measures 60°.
AB= BC = AC (All sides are equal)
Hence, ∠A = ∠B = ∠C (Opposite angles of equal sides)
Also, we know that,
∠A + ∠B + ∠C = 180°
⇒ 3∠A = 180°
⇒ ∠A = 60°
∴ ∠A = ∠B = ∠C = 60°
9) If AD is an altitude of an isosceles triangle ABC in which AB = AC. Then:
a. BD=CD
b. BD>CD
c. BD<CD
d. None of the above
Answer: a
Explanation: In ΔABD and ΔACD,
∠ADB = ∠ADC = 90°
AB = AC (Given)
AD = AD (Common)
∴ ΔABD ≅ ΔACD (By RHS congruence condition)
BD = CD (By CPCT)
10) In a right triangle, the longest side is:
a. Perpendicular
b. Hypotenuse
c. Base
d. None of the above
Answer: b
Explanation: In triangle ABC, right-angled at B.
∠B = 90
By angle sum property, we know:
∠A + ∠B + ∠C = 180
Hence, ∠A + ∠C = 90
So, ∠B is the largest angle.
Therefore, the side (hypotenuse) opposite to largest angle will be longest one.