In figure, what is $z$ in terms of $x$ and $y?$
- A$180^\circ - (x + y)$
- B$x + y + 180^\circ $
- C$x + y + 360^\circ $
- ✓$x + y - 180^\circ $
Answer: D.
View full solution →Question types
Triangles question types
420 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
420
Questions
9
Question groups
5
Question types
01
M.C.Q
273 Q→02Assertion (A) & Reason (B) MCQ
58 Q→03True False[1 Marks ]
25 Q→04Fill In The Blanks[1 Marks ]
27 Q→051 Marks Question
9 Q→062 Marks Questions
13 Q→073 Marks Question
7 Q→085 Marks Questions
2 Q→09Case study (4 Marks)
6 Q→Sample Questions
Triangles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In $\triangle\text{ABC, AB=AC}$ and $\angle\text{B}=50^\circ.$ Then $\angle\text{A}=?.$
- A$40$
- B$50$
- C$130$
- ✓$80$
Answer: D.
View full solution →In the given figure $AB > AC$. If $BO$ and $CO$ are the bisectors of $\angle\text{B}$ and $\angle\text{C}$ respectively then,
- ANone of these
- B$OB = OC$
- C$OB < OC$
- ✓$OB > OC$
Answer: D.
View full solution →In the adjoining figure, $ABCD$ is a quadrilateral in which $BN$ and $DM$ are drawn perpendiculars to $AC$ such that $BN = DM$. If $OB = 4cm$. then $BD$ is:
- A$6\ cm$
- ✓$8\ cm$
- C$10\ cm$
- D$12\ cm$
Answer: B.
View full solution →In the adjoining fig. $AB = AC$. If $\angle\text{C} = 50^\circ,$ then the value of $x$ and $y$ are:
- A$x = 50^{\circ}$ and $y = 80^{\circ}$
- B$x = 60^{\circ}$ and $y = 70^{\circ}$
- C$x = 70^{\circ}$ and $y = 60^{\circ}$
- ✓$x = 80^{\circ}$ and $y = 50^{\circ}$
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In a right triangle, the longest side is hypotenus.
Reason: The side opposite to the largest angle will be the smallest one.
Assertion: In a right triangle, the longest side is hypotenus.
Reason: The side opposite to the largest angle will be the smallest one.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If we draw two triangles with angles $30^\circ , 70^\circ $ and $80^\circ $ and the length of the sides of one triangle be different than that of the corresponding sides of the other triangle then two triangles are not congruent.
Reason: If two triangles are constructed which have all corresponding angles equal but have unequal corresponding sides, then two triangles cannot be congruent to each other.
Assertion: If we draw two triangles with angles $30^\circ , 70^\circ $ and $80^\circ $ and the length of the sides of one triangle be different than that of the corresponding sides of the other triangle then two triangles are not congruent.
Reason: If two triangles are constructed which have all corresponding angles equal but have unequal corresponding sides, then two triangles cannot be congruent to each other.
- ✓Both assertion and reason are true and reason is the correct explanation of assertion.
- BBoth assertion and reason are true but reason is not the correct explanation of assertion.
- CAssertion is true but reason is false.
- DAssertion is false but reason is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Equiangular means equal angles.
Reason: All isosceles triangle are equilangular.
Assertion: Equiangular means equal angles.
Reason: All isosceles triangle are equilangular.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\triangle\text{ABC}$ and $\triangle\text{DBC}$ are two isosceles triangles on the same base $BC$ and vertices $A$ and $D$ are on the same side of $BC$. If $AD$ is extended to intersect $BC$ at $E$, then $\triangle\text{ABD} \cong \triangle\text{ACD}.$
Reason:
If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent.
Assertion: $\triangle\text{ABC}$ and $\triangle\text{DBC}$ are two isosceles triangles on the same base $BC$ and vertices $A$ and $D$ are on the same side of $BC$. If $AD$ is extended to intersect $BC$ at $E$, then $\triangle\text{ABD} \cong \triangle\text{ACD}.$
Reason:
If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In $ \triangle\text{ABC},$ $\angle\text{C}=\angle\text{A},$ $BC = 4\ cm$ and $AC = 5\ cm$. Then, $AB = 4\ cm$.
Reason: In a triangle, angles opposite to two equal sides are equal.
Assertion: In $ \triangle\text{ABC},$ $\angle\text{C}=\angle\text{A},$ $BC = 4\ cm$ and $AC = 5\ cm$. Then, $AB = 4\ cm$.
Reason: In a triangle, angles opposite to two equal sides are equal.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: B.
View full solution →If the bisector of the verical angle of a triangle bisects the base, then the triangle may be isosceles.
An exterior angle of a triangle is equal to the sum of the two interior opposite angles.
An exterior angle of a triangle is greater than the opposite interior angles.
Sum of the three angles of a triangle is $180^\circ .$
View full solution →All the angles of a triangle can be equal to $60^\circ .$
View full solution →Medians of an equilateral triangle are .
Difference of any two sides of a triangle is ___ than the third side.
In right triangles $ABC$ and $DEF,$ if hypotenuse $\text{AB}=\text{EF}$ and side $\text{AC}=\text{DE},$ then $\triangle\text{ABC}\cong\triangle$ ________.
View full solution →An exterior angle of a triangle is equal to the two ______ opposite angles.
Drawing a $\triangle\text{ABC}$ with $AB = 3\ cm, BC = 4\ cm$ and $CA = 7\ cm$ is .
View full solution →$ABC$ is an isosceles triangle in which altitudes $BE$ and $CF$ are drawn to sides $AC$ and $AB$ respectively (See figure). Show that these altitudes are equal.
View full solution →Line $l$ is the bisector of an angle $\angle A$ and $B$ is any point on $l. BP$ and $BQ$ are perpendicular from $B$ to the arms of $\angle A.$
Show that:
$i. \triangle APB \cong \triangle AQB$
$ii. BP = BQ$ or $B$ is equidistant from the arms of $\angle A.$
View full solution →Show that:
$i. \triangle APB \cong \triangle AQB$
$ii. BP = BQ$ or $B$ is equidistant from the arms of $\angle A.$
$l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$. Show that $\Delta ABC \cong \Delta CDA.$
View full solution →$AD$ and $BC$ are equal perpendiculars to a line segment $AB.$ Show that $CD$ bisects $AB ($See figure$)$
View full solution →$D$ is a point on side $BC$ of $\triangle ABC$ such that $AD = AC ($see Fig.$).$ Show that $AB > AD.$
View full solution →ABC is an isosceles triangle with AB = AC. Draw AP $\perp$ BC to show that $\angle$B = $\angle$C.
View full solution →$B E$ and $C F$ are two equal altitudes of a triangle $A B C$. Using $RHS$ congruence rule, prove that a triangle $A B C$ is isosceles.
View full solution →ABC is a right-angled triangle in which $\angle A =90^{\circ}$ and $AB = AC$. Find $\angle B$ and $\angle C$.
View full solution →$ABC$ and $DBC$ are two isosceles triangles on the same base $BC$. Show that $\angle ABD = \angle ACD.$
View full solution →$ABC$ is a triangle in which altitudes BE and $CF$ to sides $AC$ and $AB$ are equal. Show that $\triangle \mathrm { ABE } \cong \triangle \mathrm { ACF }, AB = AC$ i.e. $\triangle$ABC is an isosceles triangle.
View full solution →Two sides $AB$ and $BC$ and median $AM$ of the $\triangle ABC$ are respectively equal to side $PQ$ and $QR$ and median $PN $of $\text{PQR} ($See figure$)$. Show that:
$i. \triangle ABM \cong \triangle PQN$
$ii. \triangle ABC \cong \triangle PQR$
View full solution →$i. \triangle ABM \cong \triangle PQN$
$ii. \triangle ABC \cong \triangle PQR$
$AD$ is an altitude of an isosceles $\triangle ABC$ in which $AB = AC$. Show that
$i. AD$ bisects $BC$
$ii. AD$ bisects $\angle A.$
View full solution →$i. AD$ bisects $BC$
$ii. AD$ bisects $\angle A.$
Show that the angles of an equilateral triangle are $60^\circ $ each.
View full solution →$\Delta ABC$ is an isosceles triangle in which $AB = AC$. Side $BA$ is produced to $D$ such that $AD = AB$ (See figure). Show that $\angle BCD$ is a right angle.
View full solution →In an isosceles triangle $ABC$ , with $AB = AC$, the bisectors of $\angle B$ and $\angle C$ intersect each other at $O$ . Join A to $O$ . Show that $O B=O C$ and $A O$ bisects $\angle A$.
View full solution →$\triangle ABC$ and $\triangle DBC$ are two isosceles triangles on the same base $BC$ and vertices $A$ and $D$ are on the same side of $BC$ . If $A D$ is extended to intersect $B C$ at $P$, show that :
$1. \triangle ABD \cong \triangle ACD$
$2. \triangle ABP \cong \triangle ACP$
$3. AP$ bisects $\angle A$ as well as $\angle D$
$4. AP$ is the perpendicular bisector of $BC.$
View full solution →$1. \triangle ABD \cong \triangle ACD$
$2. \triangle ABP \cong \triangle ACP$
$3. AP$ bisects $\angle A$ as well as $\angle D$
$4. AP$ is the perpendicular bisector of $BC.$
Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.
In the given figure, the isosceles triangle $ABC ≅ EAD.$ The point $E$ is equidistant from both $A$ and $B.$
$4.$ What is the value of $x?$
$A. 40^\circ $
$B. 60^\circ $
$C. 70^\circ $
$D. 80^\circ $
$5.$ What is the value of $y?$
$6.$ What is the value of $\angle BDC?$
$A. 30^\circ $
$B. 40^\circ $
$C. 50^\circ $
$D. 70^\circ $
View full solution →$4.$ What is the value of $x?$
$A. 40^\circ $
$B. 60^\circ $
$C. 70^\circ $
$D. 80^\circ $
$5.$ What is the value of $y?$
$6.$ What is the value of $\angle BDC?$
$A. 30^\circ $
$B. 40^\circ $
$C. 50^\circ $
$D. 70^\circ $
In the given figure, $\triangle AFB ≅ \triangle AFG, \triangle ADE ≅ AGE$ and $\angle EAF = 45^\circ .$
$1.$ What is the measure of $\angle DAB?$
$A. 60^\circ $
$B. 90^\circ $
$C. 120^\circ $
$D. 135^\circ $
$2.$ What is the length of $AD?$
$3.$ What is the area of the shaded region$?$
$A. 12.5\ cm^2$
$B. 15\ cm^2$
$C. 20\ cm^2$
$D. 36\ cm^2$
View full solution →$1.$ What is the measure of $\angle DAB?$
$A. 60^\circ $
$B. 90^\circ $
$C. 120^\circ $
$D. 135^\circ $
$2.$ What is the length of $AD?$
$3.$ What is the area of the shaded region$?$
$A. 12.5\ cm^2$
$B. 15\ cm^2$
$C. 20\ cm^2$
$D. 36\ cm^2$
Read the Source/ Text given below and answer any four questions: In a forest, a big tree got broken due to heavy rain and wind. Due to this rain the big branches $AB$ and $AC$ with lengths $5\ m$ fell down on the ground. Branch $AC$ makes an angle of $30^\circ $ with the main tree $AP.$ The distance of Point $B$ from $P$ is $4\ m.$ You can observe that $\triangle\text{ABP}$ is congruent to $\triangle\text{ACP}.$
Now answer the following questions:
$i. \triangle\text{ACP}$ and $\triangle\text{ABP}$ are congruent by which criteria?
$a. \text{SSS}$
$b. \text{SAS}$
$c.\text{ASA}$
$d. \text{RHS}$
$ii.$ What is the length of $CP?$
$a.4\ m$
$b.5\ m$
$c.3\ m$
$d.10\ m$
$iii.$ What is the value of $\angle\text{BAP}?$
$a.40^\circ $
$b.50^\circ $
$c.30^\circ $
$d.60^\circ $
$iv.$ What is the value of $\angle\text{APB}?$
$a.40^\circ $
$b.50^\circ $
$c.60^\circ $
$d.90^\circ $
$v.$ What is the height of the remaining tree$?$
$a.4\ m$
$5\ m$
$c.3\ m$
$d.10\ m$
View full solution →Now answer the following questions:
$i. \triangle\text{ACP}$ and $\triangle\text{ABP}$ are congruent by which criteria?
$a. \text{SSS}$
$b. \text{SAS}$
$c.\text{ASA}$
$d. \text{RHS}$
$ii.$ What is the length of $CP?$
$a.4\ m$
$b.5\ m$
$c.3\ m$
$d.10\ m$
$iii.$ What is the value of $\angle\text{BAP}?$
$a.40^\circ $
$b.50^\circ $
$c.30^\circ $
$d.60^\circ $
$iv.$ What is the value of $\angle\text{APB}?$
$a.40^\circ $
$b.50^\circ $
$c.60^\circ $
$d.90^\circ $
$v.$ What is the height of the remaining tree$?$
$a.4\ m$
$5\ m$
$c.3\ m$
$d.10\ m$
Read the Source/ Text given below and answer these questions:
Hareesh and Deep were trying to prove a theorem. For this they did the following:
$i.$ Drew a $\triangle ABC.$
$ii. D$ and $E$ are found as the mid points of $AB$ and $AC.$
$iii. DE$ was joined and $DE$ was extended to $F$ so $DE = EF.$
$iv. FC$ was joined.
Answer the following questions:
$i. \triangle\text{ADE}$ and $\triangle\text{EFC}$ are congruent by which criteria$?$
$\text{SSS}$
$\text{RHS}$
$\text{SAS}$
$\text{ASA}$
$ii. \angle\text{EFC}$ is equal to which angle$?$
$a. \angle\text{DAE}$
$b. \angle\text{ADE}$
$c. \angle\text{AED}$
$d. \angle\text{B}$
$iii. \angle\text{ECF}$ is equal to which angle$?$
$a. \angle\text{DAE}$
$b. \angle\text{ADE}$
$c. \angle\text{AED}$
$d. \angle\text{B}$
$iv. CF$ is equal to which of the following$?$
$a. BD$
$b. CE$
$c. AE$
$d. EF$
$v. CF$ is parallel to which of the following$?$
$a. AE$
$b. CE$
$c. BD$
$d. EF$
View full solution →Hareesh and Deep were trying to prove a theorem. For this they did the following:
$i.$ Drew a $\triangle ABC.$
$ii. D$ and $E$ are found as the mid points of $AB$ and $AC.$
$iii. DE$ was joined and $DE$ was extended to $F$ so $DE = EF.$
$iv. FC$ was joined.
Answer the following questions:
$i. \triangle\text{ADE}$ and $\triangle\text{EFC}$ are congruent by which criteria$?$
$\text{SSS}$
$\text{RHS}$
$\text{SAS}$
$\text{ASA}$
$ii. \angle\text{EFC}$ is equal to which angle$?$
$a. \angle\text{DAE}$
$b. \angle\text{ADE}$
$c. \angle\text{AED}$
$d. \angle\text{B}$
$iii. \angle\text{ECF}$ is equal to which angle$?$
$a. \angle\text{DAE}$
$b. \angle\text{ADE}$
$c. \angle\text{AED}$
$d. \angle\text{B}$
$iv. CF$ is equal to which of the following$?$
$a. BD$
$b. CE$
$c. AE$
$d. EF$
$v. CF$ is parallel to which of the following$?$
$a. AE$
$b. CE$
$c. BD$
$d. EF$
Read the Source/ Text given below and answer any four questions:
As shown In the village of Surya there was a big pole $PC.$ This pole was tied with a strong wire of $10\ m$ length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of $10\ m$ so that it can reach at point $P$ on the pole and this should make $60^\circ $ with line $AC.$ Answer the following questions:
$i.$ In the $\triangle\text{PAC}$ and $\triangle\text{PBC}$ which side is common?
$a. PC$
$b. AB$
$c. AC$
$d. BC$
$ii.$ In the $\triangle\text{PAC}$ and $\triangle\text{PBC}$ which angles are given to be equal?
$a. \angle\text{A}=\angle\text{X}$
$b. \angle\text{B}=\angle\text{X}$
$c. \angle\text{B}=\angle\text{Y}$
d. None
$iii.$ In the figure, $\triangle\text{PAC}$ and $\triangle\text{PBC}$ are congruent due to which criteria$?$
$a. \text{RHS}$
$b. \text{SAS}$
$c. \text{SSS}$
$d. \text{ASA}$
$iv.$ What is the value of $\angle\text{PBC}\text{?}$
$a. 30^\circ $
$b. 60^\circ $
$c. 90^\circ $
$d. 45^\circ $
$v.$ What is the value of $\angle\text{X}\text{?}$
$a. 45^\circ $
$b. 60^\circ $
$c. 90^\circ $
$d. 30^\circ $
View full solution →As shown In the village of Surya there was a big pole $PC.$ This pole was tied with a strong wire of $10\ m$ length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of $10\ m$ so that it can reach at point $P$ on the pole and this should make $60^\circ $ with line $AC.$ Answer the following questions:
$i.$ In the $\triangle\text{PAC}$ and $\triangle\text{PBC}$ which side is common?
$a. PC$
$b. AB$
$c. AC$
$d. BC$
$ii.$ In the $\triangle\text{PAC}$ and $\triangle\text{PBC}$ which angles are given to be equal?
$a. \angle\text{A}=\angle\text{X}$
$b. \angle\text{B}=\angle\text{X}$
$c. \angle\text{B}=\angle\text{Y}$
d. None
$iii.$ In the figure, $\triangle\text{PAC}$ and $\triangle\text{PBC}$ are congruent due to which criteria$?$
$a. \text{RHS}$
$b. \text{SAS}$
$c. \text{SSS}$
$d. \text{ASA}$
$iv.$ What is the value of $\angle\text{PBC}\text{?}$
$a. 30^\circ $
$b. 60^\circ $
$c. 90^\circ $
$d. 45^\circ $
$v.$ What is the value of $\angle\text{X}\text{?}$
$a. 45^\circ $
$b. 60^\circ $
$c. 90^\circ $
$d. 30^\circ $
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