Mathematics - Triangles
Exam Duration: 45 Mins Total Questions : 30
One of the angles of a triangle is 75o If the difference of the other two angles is 35o what is the measure the largest angle of the triangle?
- (a)
80o
- (b)
75o
- (c)
100o
- (d)
100o
In quadrilateral ACBD,AB is a diagonal. If AC = AD and AB bisects \(\angle A\), by which congruence property is ∆ACB ≌ ∆ADB ?
- (a)
S.A.S
- (b)
A.S.A
- (c)
S.S.S
- (d)
R.H.S
In the given figure, ∠O < ∠P and ∠R < ∠S. Which of the following is true?
- (a)
PS< OR
- (b)
PS > OR
- (c)
OR = PS
- (d)
Either (B) or (C)
In the given figure, if AB = AC and BD = DC, by which criterion are \(\triangle\)ABD and \(\triangle\)ACD congruent?
- (a)
S.S.S
- (b)
A.S.A
- (c)
S.A.S
- (d)
R.H.S
\(\triangle\)ABC is an isosceles triangle with AB = AC. If AD⊥ BC, which of the following is true?
- (a)
\(\angle B\)>\(\angle C\)
- (b)
\(\angle B\)=\(\angle C\)
- (c)
\(\angle B\)<\(\angle C\)
- (d)
\(\angle A\)=\(\angle B\)=\(\angle C\)
In the given figure, if AD = BC and AD || BC, which of the following holds good?
- (a)
AB = AD
- (b)
AB = DC
- (c)
BC = CD
- (d)
AB = AC
A : Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other.
R : Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other. Which of the following statements is correct?
- (a)
A is false and R is the correct explanation of A
- (b)
A is true and R is the correct explanation of A.
- (c)
A is true and R is false
- (d)
A is false and R is false
Which of the following statements is true?
- (a)
Two line segments having the same length are congruent.
- (b)
Two squares having the same side length are congruent.
- (c)
Two circles having the same radius are congruent.
- (d)
All the above
In \(\triangle\)ABC, if AB = BC, which of the following statements is necessarily true?
- (a)
\(\angle B\) = \(\angle C\)
- (b)
\(\angle A\) = \(\angle C\)
- (c)
\(\angle A\) = \(\angle B\)
- (d)
\(\angle A\) < \(\angle C\)
In \(\triangle \)ABC, AB = 5 cm, BC = 6 cm and CA = 7 cm. Identify the relation between the angles.
- (a)
∠B > ∠A > ∠C
- (b)
∠A > ∠B > ∠C
- (c)
∠B > ∠C > ∠A
- (d)
∠B > ∠A > ∠C
In triangles ABC and DEF,AB = FD and ∠A =∠D.Which of the following is true if the two triangles are congruent by S.A.S. axiom?
- (a)
BC = EF
- (b)
AC = DE
- (c)
AC = EF
- (d)
BC = DE
If \(\triangle \)ABC ≌ \(\triangle \)DEF by S.S.S.congruence rule, which of the following options holds true?
- (a)
∠A > ∠D
- (b)
∠A = ∠D,∠B = ∠E ,∠C= ∠F
- (c)
∠B < ∠F
- (d)
∠C = ∠F
If \(\triangle \)ABC ≌ \(\triangle \)DEF by S.S.S.congruence ruIe, which of the following statements is true?
- (a)
AB = EF,BC = FD,CA = DE
- (b)
AB = FD,BC = DE,CA = EF
- (c)
AB = DE.BC = EF,CA = FD
- (d)
AB = DE,BC = EF =∠C =∠F
In \(\triangle \)ABD, if ∠B = ∠C, which of the following is true?
- (a)
BC = AB
- (b)
AC = BC
- (c)
AB = AC
- (d)
AB > AC
In \(\triangle \)ABC, ∠A = 50o. ∠B = 60o. What is the ascending order of the sides of the triangle?
- (a)
AB < BC < CA
- (b)
CA < AB < BC
- (c)
BC < CA < AB
- (d)
BC < AB < CA
In \(\triangle \)DEF, which of the following statements is true
- (a)
DE + EF= FD
- (b)
DE + EF< FD
- (c)
DE > EF+ FD
- (d)
DE + EF > FD
In \(\triangle \)ABC, if AD is the perpendicular bisector of BC, which of the following is true?
- (a)
AB > AC
- (b)
AD = AB
- (c)
AB = AC
- (d)
AD = AC
In \(\triangle \)ABC, if AD is a median, what is the relation between the sides?
- (a)
AB + AC > AD
- (b)
AB + AC < 2AD
- (c)
AB + AC = 2AD
- (d)
AB + AC > 2AD
An exterior angle of a triangle is 120o and the two interior opposite angles are equal. Find the value of each interior angle
- (a)
60o
- (b)
100o
- (c)
120o
- (d)
180o
In a right triangle, the two acute angles are in the ratio 4: 5. Find them respectively
- (a)
50o,40o
- (b)
40o,50o
- (c)
45o,55o
- (d)
30o,60o
In the figure given, AB = AC,E is midpoint of AB and F is midpoint of AC. What is the length of BF?
- (a)
AE
- (b)
CF
- (c)
BE
- (d)
CE
In the given figure, AP \(\bot\) QR, PR > PQ and PS = PQ. Then
- (a)
AP = QP
- (b)
AP > AQ
- (c)
\(\angle APS>\angle APQ\)
- (d)
AR > AQ
In the given figure, x and y are _________.
- (a)
x = 70°, y = 37°
- (b)
x = 37°, y = 70°
- (c)
x + y = 117°
- (d)
x - y = 100°
If the given triangles are congruent, then which of the following options is CORRECT?
- (a)
\(\Delta ABC\equiv \Delta DEF\)
- (b)
\(\Delta ABC\equiv \Delta EDF\)
- (c)
\(\Delta ABC\equiv \Delta FDE\)
- (d)
\(\Delta ACB\equiv \Delta EDF\)
In \(\Delta DEF\) and \(\Delta PQR\), DE = DF, \(\angle F\) = \(\angle P\) and \(\angle E\) = \(\angle Q\). The two triangles are
- (a)
Isosceles but not necessarily congruent
- (b)
Isosceles and congruent
- (c)
Congruent but not isosceles
- (d)
Neither congruent nor isosceles
Which of the following is not a critertion for congruence of triangles?
- (a)
SAS
- (b)
ASA
- (c)
SSA
- (d)
SSS
D is any point on side AC of a \(\Delta ABC\) with AB = AC. Then _______.
- (a)
CD < BD
- (b)
CD > BD
- (c)
CD = BD
- (d)
None of these
If AD is bisector of \(\angle A\) and D is perpendicular to BC. Then \(\Delta ABC\) is ________ triangle.
- (a)
Isosceles
- (b)
Equilateral
- (c)
Scalene
- (d)
None of these
Which of the following statement is CORRECT?
- (a)
Two triangles having same shape are congruent.
- (b)
If two sides of a triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent.
- (c)
If the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of the other triangle, then the triangles are not congruent.
- (d)
None of these
ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Then AC + AD = _________.
- (a)
BC
- (b)
2BC
- (c)
3BC
- (d)
None of these