Content Curator
A triangle is a plane figure formed by the three-non parallel line segments. A triangle is named on the basis of the length of the sides and the measure of their angles. To make your exam prep easier we have provided practice MCQs on the topic ‘Triangles’. Triangles are a part of the class-9 NCERT Mathematics book and are also included in various entrance exams.
Also Read: Triangle
Question: In triangle ABC, AB=BC and ∠B = 70°. Find ∠A
- 70°
- 110°
- 55°
- 130°
Click here for the answer
Answer: c
Explanation:
In triangle ABC
AB=BC (Triangle ABC is an Isosceles Triangle)
So, ∠A = ∠C (Opposite angles and sides are equal in an Isosceles Triangle)
∠A= ∠C and ∠B = 70°
Using angle sum property of triangle, we know:
∠A+∠B+∠C = 180°
2∠A+∠B=180°
2∠A = 180-∠B = 180-70 = 110°
∠A = 55°
Question: E and F are midpoints of equal sides AB and AC of triangle ABC. Then:
- BF=AC
- BF=AF
- CE=AB
- BF=CE
Click here for the answer
Answer: d
Explanation: In triangle ABC
AB=AC (Triangle ABC is an Isosceles Triangle)
∠A =∠A (Angle is common)
AE=AF (Half of the equal sides that is AB and AC)
Using Side Angle Side Property,
ABF ≅ ACE
So, BF=CE (corresponding sides of corresponding triangles)
Question: In an Isosceles Triangle ABC altitude BE and CF is drawn to the equal sides of the isosceles triangle – AB and AC respectively, then:
- BE>CF
- BE<CF
- BE= CF
- None of these
Click here for the answer
Answer: c
Explanation: In triangle ABC
AB=AC (Triangle ABC is an Isosceles Triangle)
∠A =∠A (Angle is common)
∠AEB =∠AFC = 90° (BE and CF are altitudes)
Using Angle Angle Side (AAS) Property,
ΔAEB ≅ ΔAFC
So, BE = CF (corresponding sides of corresponding triangles)
Question: If triangle ABC and DBC are two isosceles triangles on the same base BC. Then:
- ∠ABD = ∠ACD
- ∠ABD > ∠ACD
- ∠ABD < ∠ACD
- None of these
Click here for the answer
Answer: a
Explanation: In triangle ABC
AB=AC (Triangle ABC is an Isosceles Triangle)
AD=AD (Common arm)
BD=CD (Triangle DBC is an Isosceles Triangle)
Using Side Angle Side Property,
So,
ΔABD ≅ ΔACD.
∴∠ABD = ∠ACD (corresponding sides of corresponding triangles)
Question: If triangle ABC is an equilateral triangle, then each angle equals to:
- 90°
- 180°
- 120°
- 60°
Click here for the answer
Answer: d
Explanation: Triangle ABC is an equilateral triangle,
In an equilateral triangle, all sides are equal to each other
So, AB=BC=AC
Thus, all angles are also equal to each other
∠A=∠B=∠C
By angle sum property of triangle:
∠A+∠B+∠C = 180°
3∠A = 180° (∠A=∠B=∠C)
∠A = 60°
Thus, each angle measures 60°.
Question: AD is an altitude of an isosceles triangle, then:
- BD=CD
- BD>CD
- BD<CD
- None of these
Click here for the answer
Answer: a
Explanation: In triangle ABC
AB=AC (Triangle ABC is an Isosceles Triangle)
Now in triangle ABD and triangle ACD
∠ADB = ∠ADC = 90° (AD is an altitude)
AD=AD (common side in triangle ABD and triangle ACD)
AB=AC (Triangle ABC is an Isosceles Triangle)
Using RHS Congruence property
ΔABD ≅ ΔACD
BD=CD (corresponding sides of corresponding triangles)
Question: In a right-angle triangle ABC, the longest side is:
- Perpendicular
- Hypotenuse
- Base
- None of these
Click here for the answer
Answer: b
Explanation: In a right triangle ABC
∠B=90° (the right angle at B)
Using angle sum property of triangle, we know:
∠A+∠B+∠C = 180°
∠A+90°+∠C = 180°
∠A+∠C = 90°
Clearly, ∠B is the largest angle in the triangle
Since the side opposite to the largest angle is the longest
The hypotenuse is the longest side of the right-angle triangle ABC.
Also Read:
Question: In triangles ABC and PQR, AB = AC, ∠C=∠P, and ∠B=∠Q then, The two triangles are
- Isosceles and congruent
- Only Isosceles
- Only Congruent
- None of these
Click here for the answer
Answer: b
Explanation: The two triangles ABC and PQR are
We know that
∠A + ∠B + ∠C = ∠P + ∠Q + ∠R
It is given that
∠C = ∠P and ∠B = ∠Q … (1)
We get
∠A + ∠B + ∠C = ∠C + ∠B + ∠R
Here ∠A = ∠R
Using the AAA criterion
∆ ABC ≅ ∆ PQR
As AB = AC, ∆ ABC is an isosceles triangle
∠B = ∠C [opposite angles of equal sides]
From (1), ∠P = ∠Q
So ∆ PQR is an isosceles triangle
As the relation between sides of two triangles is unknown, congruency cannot be proved using SAS or ASA
Therefore, the two triangles are isosceles but not congruent.
Question: In triangle PQR,∠R = ∠P, QR=4 and PR = 5. Find PQ.
- 2
- 2.5
- 4
- 5
Click here for the answer
Answer: C
Explanation: In triangle PQR
∠R = ∠P, QR=4 and PR = 5
As ∠R = ∠P
PQ=QR (Equal angles have equal sides)
PQ=QR= 4
Question: If AB=BC, BC=PR, CA=PQ, then,
- PQR ≅ BCA
- BAC ≅ RPQ
- CBA ≅ PRQ
- ABC ≅ PQR
Click here for the answer
Answer: c
Explanation: In triangle ABC and PQR,
AB=BC (given)
BC=PR (given)
CA=PQ (given)
Using Side-Side-Side Congruence Property,
CBA ≅ PRQ.
Question: In triangle ABC, BC=AB and ∠B = 80°. Find ∠A
- 40°
- 50°
- 80°
- 100°
Click here for the answer
Answer: b
Explanation:
In triangle ABC
AB=BC (Triangle ABC is an Isosceles Triangle)
So, ∠A = ∠C (Opposite angles and sides are equal in an Isosceles Triangle)
∠A= ∠C and ∠B = 80°
Using angle sum property of triangle, we know:
∠A+∠B+∠C = 180°
2∠A = 100°
∠A = 50°
Question: The sides of a triangle are of lengths 5cm and 1.5 cm. The length of the third side cannot be:
- 3.4
- 3.6
- 3.8
- 4.1
Click here for the answer
Answer: a
Explanation: The sides of the triangle are of lengths 5cm and 1.5 cm. The sum of two sides of a triangle is more than the third side. The difference between the two sides should be less than the third side.
Question: In triangle ABC, AB=AC and ∠B = 40°. Find ∠A
- 40°
- 70°
- 80°
- 130°
Click here for the answer
Answer: b
Explanation:
In triangle ABC
AB=AC (Triangle ABC is an Isosceles Triangle)
So, ∠A = ∠C (Opposite angles and sides are equal in an Isosceles Triangle)
∠A= ∠C and ∠B = 50
Using angle sum property of triangle, we know:
∠A+∠B+∠C = 180°
2∠C = 140°
∠C = 70°
Question: If ABC ≅ FDE, ∠B = 40° and ∠A = 80°. Which of the following is true?
- DF= 5cm and ∠F = 60°
- DF= 5cm and ∠E = 60°
- DE= 5cm and ∠E = 60°
- DE= 5cm and ∠D= 40°
Click here for the answer
Answer: b
Explanation: ABC ≅ FDE
∠B = 40° and ∠A = 80°
Using the CPCT rule
DF =AB=5cm
∠E =∠C
Using angle sum property of triangle, we know:
∠E+∠F+∠D = 180°
∠E = 180° - 120°
∠E = 60°
For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates
Also Check:
Comments