Which one of the following pairs of triangles is not a congruent pair?
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Triangles [NEW] question types
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210
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10
Question groups
5
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01
M.C.Q
111 Q→02Assertion (A) & Reason (B) MCQ
16 Q→03Fill In The Blanks[1 Marks ]
15 Q→04True False[1 Marks ]
11 Q→051 Marks Question
10 Q→062 Marks Questions
13 Q→073 Marks Question
10 Q→084 Marks Questions
15 Q→09Case study (4 Marks)
2 Q→105 Marks Questions
7 Q→Sample Questions
Triangles [NEW] questions
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Which of the following is not a criterion for congruence of triangles?
- ASAS
- ✓SSA
- CASA
- DSSS
Answer: B.
View full solution →Which of the following is not a criterion for congruence of triangles?
- ASAS
- BASA
- CSSA
- DSSS
The side BC of $\triangle A B C$ is produced to a point D. The bisector of $\angle A$ meets side BC in L. If $\angle A B C=30^{\circ}$ and $\angle A C D=115^{\circ}$, then $\angle A L C=$
- A$85^{\circ}$
- ✓$72 \frac{1}{2}^{\circ}$
- C$145^{\circ}$
- Dnone of these
Answer: B.
View full solution →The side BC of $\triangle\text{ABC}$ is produced to a poin D. The bisector of $\angle\text{A}$ meet side BC in L. If $\angle\text{ABC}=30^\circ$ and $\angle\text{ACD}=115^\circ,$ then $\angle\text{ALC}=$
View full solution →- $85^\circ$
- $72\frac{1}{2}^\circ$
- $145^\circ$
-
$\text{None of these}$
Statement-1 (A): The sum of any two sides of a triangle is greater than the third side.
Statement-2 (R): It is possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm.
Statement-2 (R): It is possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Statement-1 (A): It is possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm .
Statement-2 (R): The sum of any two sides of a triangle is greater than the third side.
Statement-2 (R): The sum of any two sides of a triangle is greater than the third side.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): It is not possible to construct a triangle with lengths of its sides as 9 cm , 7 cm and 17 cm .
Statement-2 (R): The difference of any two sides of a triangles is less than the third side.
Statement-2 (R): The difference of any two sides of a triangles is less than the third side.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): In Fig., side BC of $\triangle A B C$ is produced to D. If $\angle A C D=110^{\circ}$, then $x=40^{\circ}$.
Statement-2 (R): If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.
Statement-2 (R): If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): In Fig. side $B C$ of $\triangle A B C$ is produced to a point $D$ such that the bisectors of $\angle A B C$ and $\angle A C D$ meet at a point $E$. If $\angle B A C=80^{\circ}$, then $\angle B E C=50^{\circ}$.
Statement-2 (R): The angle between the internal bisector of one base angle and the external bisector of the other angle of a triangle is equal to one-half of the vertical angle.
Statement-2 (R): The angle between the internal bisector of one base angle and the external bisector of the other angle of a triangle is equal to one-half of the vertical angle.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- ✓Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle lies between ____________ and ____________ .
It is given that $\triangle A B C \cong \triangle R P Q$, then BC = ____________ .
View full solution →In triangles ABC and DEF, AB = FD and $\angle A=\angle D$. The two triangles will be congruent by SAS axiom, if ____________ .
View full solution →In $\triangle P Q R$, if $\angle R>\angle Q$, then ____________ .
View full solution →In $\triangle P Q R, \angle P=\angle R, Q R=4 cm$ and $P R=5 cm$. Then $P Q$ = ____________ .
View full solution →Which of the following statements are true (T) and which are false (F):
A triangle can have at most one obtuse angles.
A triangle can have at most one obtuse angles.
The following statements are true (T) and which are false (F):
Sum of the three angles of a triangle is 180°.
Sum of the three angles of a triangle is 180°.
The following statements are true (T) and which are false (F):
If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
The following statements are true (T) and which are false (F):
A triangle can have two right angles.
A triangle can have two right angles.
The following statements are true (T) and which are false (F):
A triangle can have two obtuse angles.
A triangle can have two obtuse angles.
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
In two triangles ABC and DEF, it is given that $\angle A = \angle D, \angle B = \angle E$ and $\angle C = \angle F$. Arethe two triangles necessarily congruent?
View full solution →In two triangles ABC and ADC, if AB = AD and BC = CD Are they congruent?
In two congruent triangles ABC and DEF, if AB = DE and BC = EF . Name the pairs of equal angles.
In triangles ABC and CDE, if $AC = CE, BC = CD, \angle A = 60^{\circ}, \angle C = 30^{\circ}$ and $\angle D = 90^{\circ}$. Are two triangles congruent?
View full solution →Write the sum of the angles of an obtuse triangle.
State exterior angle theorem.
If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.
Define a triangle.
Compute the value of x in the following figures.
Two angles of a triangle are equal and the third angle is greater than each of those angles by 30º. Determine all the angles of the triangle.
The exterior angles, obtained on producing the base of a triangle both ways are 104° and 136°. Find all the angles of the triangle.
The angles of a triangle are (x - 40)º, (x - 20)º and $\Big(\frac{1}{2}\text{x}-10\Big)^\circ.$ Find the value of x.
View full solution →In figure AE bisects $\angle\text{CAD}$ and $\angle\text{B}=\angle\text{C}.$ Prove that AE || BC.
View full solution →In Fig. $\text{AC}\perp\text{CE}$ and $\angle\text{A}:\angle\text{B}:\angle\text{C}=3:2:1,$ find the value of $\angle\text{ECD}.$
View full solution →The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.
The bisectors of base angles of a triangle cannot enclose a right angle in any case.
The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°, find the three angles.
In the given figure, side BC of $\triangle\text{ABC}$ is produced to point D such that bisectors of $\angle\text{ACD}$ meet at a point E. If $\angle\text{BAC}=68^\circ,$ find $\angle\text{BEC}.$
View full solution →In the given figure, if $\text{AB }||\text{ DE}$ and $\text{BD }||\text{ FG}$ such that $\angle\text{FGH}=125^\circ$ and $\angle\text{B}=55^\circ,$ find x and y.
View full solution →Engineers often use the familiar triangular shape for strength in bridge design. Triangles are effective tools for architecture and are used in the design of bridges, buildings and other structures as they provide strength and stability. The triangle is common in all sorts of building supports and trusses. Following are some questions on triangles:
(i) In triangles ABC and DEF, if AB = DE, AC = EF and $\angle A=\angle E$. Then,
(a) $\triangle A B C \cong \triangle D E F$ by SAS criterion $\quad$(b) $\triangle A B C \cong \triangle E F D$ by SSS criterion
(c) $\triangle A B C \cong \triangle E D F$ by SAS criterion $\quad$(d) $\triangle A B C \cong \triangle E D F$ by ASA criterion
(ii) If $\triangle P R Q \cong \triangle D E F$, then $D E=$
(a) PR $\quad$(b) RQ $\quad$(c) PQ $\quad$(d) DF
(iii) Is it possible to construct a triangle with lengths of sides as 5 cm, 4 cm and 10 cm ?
(iv) In triangles ABC and DEF, AB = FD and $\angle A=\angle D$. Then the two triangles will be congruent by SAS axiom, if
(a) BC = EF $\quad$(b) AC = DE $\quad$(c) AC = EF $\quad$(d) BC = DE
View full solution →(i) In triangles ABC and DEF, if AB = DE, AC = EF and $\angle A=\angle E$. Then,
(a) $\triangle A B C \cong \triangle D E F$ by SAS criterion $\quad$(b) $\triangle A B C \cong \triangle E F D$ by SSS criterion
(c) $\triangle A B C \cong \triangle E D F$ by SAS criterion $\quad$(d) $\triangle A B C \cong \triangle E D F$ by ASA criterion
(ii) If $\triangle P R Q \cong \triangle D E F$, then $D E=$
(a) PR $\quad$(b) RQ $\quad$(c) PQ $\quad$(d) DF
(iii) Is it possible to construct a triangle with lengths of sides as 5 cm, 4 cm and 10 cm ?
(iv) In triangles ABC and DEF, AB = FD and $\angle A=\angle D$. Then the two triangles will be congruent by SAS axiom, if
(a) BC = EF $\quad$(b) AC = DE $\quad$(c) AC = EF $\quad$(d) BC = DE
A ladder manufacturing company manufactures foldable step ladders of aluminum as shown in Fig. The lengths of two legs AB and AC are both equal to 110 cm and the angle between the two legs is $30^{\circ}$. On the basis of the above information answer the following questions:
(i) $\angle A B C$ is equal to
(a) $70^{\circ}$ $\quad$(b) $75^{\circ}$(c) $85^{\circ}$ $\quad$(d) $60^{\circ}$
(ii) If $\angle B A C=60^{\circ}$, then $B C=$
(a) 120 cm $\quad$(b) 55 cm $\quad$(c) 110 cm $\quad$(d) 100 cm
(iii) $\triangle A B C$ is
(a) isosceles acute angled $\quad$ (b) right angled isosceles
(c) isosceles obtuse angled$\quad$(d) equilateral
(iv) In two triangles ABC and DEF, if $\angle A=\angle D, A B=D E$ and $A C=D F$, then the criterion by which two triangles are congruent is
(a) SSS $\quad$(b) ASA $\quad$(c) AAS $\quad$(d) SAS
View full solution →(i) $\angle A B C$ is equal to
(a) $70^{\circ}$ $\quad$(b) $75^{\circ}$(c) $85^{\circ}$ $\quad$(d) $60^{\circ}$
(ii) If $\angle B A C=60^{\circ}$, then $B C=$
(a) 120 cm $\quad$(b) 55 cm $\quad$(c) 110 cm $\quad$(d) 100 cm
(iii) $\triangle A B C$ is
(a) isosceles acute angled $\quad$ (b) right angled isosceles
(c) isosceles obtuse angled$\quad$(d) equilateral
(iv) In two triangles ABC and DEF, if $\angle A=\angle D, A B=D E$ and $A C=D F$, then the criterion by which two triangles are congruent is
(a) SSS $\quad$(b) ASA $\quad$(c) AAS $\quad$(d) SAS
In the given figure, compute the value of x.
In $\triangle\text{ABC},$ if bisectors of $\angle\text{ABC}$ and $\angle\text{ACB}$ intersect at O at angle of 120°, then find the measure of $\angle\text{A}.$
View full solution →In Fig. the sides BC, CA and AB of a triangle ABC have been produced to D, E and F respectively. If $\angle\text{ACD}=105^\circ$ and $\angle\text{EAF}=45^\circ,$ find all the angles of the triangle ABC.
View full solution →In Fig. $\text{AM}\perp\text{BC}$ and AN is the bisector of $\angle\text{A}.$ If $\angle\text{B}=65^\circ$ and $\angle\text{C}=33^\circ,$ find $\angle\text{MAN}.$
View full solution →In a $\triangle\text{ABC},$ the internal bisectors of $\angle\text{B}$ and $\angle\text{E}$ meet at P and the external bisectors of $\angle\text{B}$ and $\angle\text{C}$ meet at Q. Prove that $\angle\text{BPC}+\angle\text{BQC}=180^\circ.$
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