Sample QuestionsTriangles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\triangle\text{ABC}$ is a right triangle right-angled at A and $\text{AD}\perp\text{BC}.$ Then, $\frac{\text{BD}}{\text{DC}}=$
- ✓
$\Big(\frac{\text{AB}}{\text{AC}}\Big)^2$
- B
$\frac{\text{AB}}{\text{AC}}$
- C
$\Big(\frac{\text{AB}}{\text{AD}}\Big)^2$
- D
$\frac{\text{AB}}{\text{AD}}$
Answer: A.
View full solution →If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that DE = 3cm, EF = 2cm, DF = 2.5cm, BC = 4cm, then perimeter of $\triangle\text{ABC}$ is:
Answer: D.
View full solution →$\triangle\text{ABC}$ is such that AB = 3cm, BC = 2cm and CA = 2.5cm. If $\triangle\text{DEF}\sim\triangle\text{ABC}$ and EF = 4cm, then perimeter of $\triangle\text{DEF}$ is:
Answer: B.
View full solution →If $D, E, F $ are the mid-points of sides $BC, CA$ and $AB$ respectively of $\triangle\text{ABC},$ then the ratio of the areas of triangles $\text{DEF}$ and $\text{ABC}$ is:
- ✓
$1 : 4$
- B
$1 : 2$
- C
$2 : 3$
- D
$4 : 5$
Answer: A.
View full solution →In a $\triangle\text{ABC},$ point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC = 3 : 5, then $\text{Area}(\triangle\text{ADE}):\text{Area}(\Box\text{BCED})=$
Answer: B.
View full solution →Statement-1 (A): $ A B C D$ is a trapezium with $D C \| A B, E$ and $F$ are points on $A D$ and $B C$ respectively, such that $E F \| A B$. Then, $\frac{A E}{E D}=\frac{B F}{F C}$.
Statement-2 (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement- 2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A) : If in $\triangle A B C, D$ and $E$ are points on sides $A B$ and $A C$ respectively such that $D E \| B C$, then $\frac{A D}{A B}=\frac{A E}{A C}$.
Statement-2 (R): If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Slatement-1 (A): Let $\triangle A B C$ and $\triangle D E F$ be right triangles right angled at $B$ and $E$ respectively. If $A C=5 cm, B C=4 cm, D F=15 cm$ and $E F=12 cm$, then $\angle A=\angle D$ and $\angle C=\angle F$.
Statement-2 (R): If in two right triangles, hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle, then the triangles are similar.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): In $\triangle A B C$, if $A B=24 cm, B C=10 cm$ and $A C=26 cm$, then $\triangle A B C$ is a right angled triangle.
Statement-2 (R): If corresponding sides of two triangles are equal, then the triangles are similar.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: B.
View full solution →Statement-1 (A): Let $\triangle P Q R$ be a right triangle right angled at $Q$ such that the perpendicular drawn from $Q$ on hypotenuse $P R$ meets $P R$ at $S$. If $P S=4$ cm and $R S=9 cm$, then $Q S=6 cm$.
Statement-2 (R): In a right triangle, the square of the perpendicular drawn from the vertex forming right angle to the hypotenuse is equal to the product of projections of two sides on the hypotenuse.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 and Statement-2 are True; Statement- 2 is not a correct explanation for Statement-1.
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Write the truth value (T/F) of the following statements:
Two polygons are similar, if their corresponding sides are proportional.
Write the truth value (T/F) of the following statements:
Any two congruent figures are similar.
Write the truth value (T/F) of the following statements:
Any two similar figures are congruent.
Write the truth value (T/F) of each of the following statements:
Two triangles are similar, if their corresponding sides are proportional.
Write the truth value (T/F) of the following statements:
Two polygons are similar, if their corresponding angles are proportional.
If ABC is an equilateral triangle of side 2a, then the length of one of its altitude is ____________ .
In Fig. $\angle ABC=90^{\circ}$, AB : BD : DC = 3 : 1 : 3. If AC = 20cm, then AD = ____________ .
View full solution →In Fig. $\angle ABC=90^{\circ}$, AD = 15 cm and DC = 20 cm. If BD is the bisector of $\angle ABC$, then perimeter of $\triangle ABC$ is ____________ .
View full solution →In $\triangle ABC$ sides AB and AC are extended to D and E respectively, such that AB = BD and AC = CE. If BC = 6cm then DE = ____________ .
View full solution →If it is given that $\triangle A B C \sim \triangle E D F$ such that AB = 5 cm AC = 7 cm DF = 15 cm and DE = 12 cm Then, BC =____________ and EF = ____________ .
View full solution →State AAA similarity criterion.
In the adjoining figure, find AC.
In the given figure, $\triangle\text{AHK}$ is similar to $\triangle\text{ABC}.$ If AK = 10cm, BC = 3.5cm and HK = 7cm, find AC.
View full solution →Triangle ABC and DEF are similar.
If area $\big(\triangle\text{ABC}\big) =16\text{cm}^2,$ area $\big(\triangle\text{DEF}\big) =25\text{cm}^2 $ and BC = 2.3cm, find EF.
View full solution →In a $\triangle\text{ABC,D}\ \text{and E}$ are points on the sides AB and AC respectively such that DE || BC.
If AD = 4cm, DB = 4.5cm and AE = 8cm, find AC.
View full solution →In the given figure, LM = LN = 46°. Express x in terms of a, b and c where a, b, c are lengths of LM, MN and NK respectively.
If the sides of a triangle are $3\ cm, 4\ cm$ and $6\ cm$ long, determine whether the triangle is a right-angled triangle.
View full solution →In fig. $\triangle\text{ABC}$ is a triangle such that $\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}},\angle\text{B}=70^\circ,\angle\text{C}=50^\circ.$ Find the $\angle\text{BAD}.$
View full solution →In the given figure, DE || BC such that $\text{AE}=\Big(\frac{1}{4}\Big)$ AC. If AB = 6cm, find AD.
View full solution →In $\triangle\text{ABC and }\triangle\text{DEF},$ it is being given that: AB = 5cm, BC = 4cm and CA = 4.2cm; DE = 10cm, EF = 8cm and FD = 8.4cm. If $\text{AL}\perp\text{BC}$ and $\text{DM} \perp \text{EF,}$ find AL : DM.
View full solution →In the given figure, $\angle\text{ABC}=90^\circ$ and $\text{BD}\perp\text{AC}.$ If BD = 8cm and AD = 4cm, find CD.
View full solution →In $\triangle\text{ABC},$ D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of $\triangle\text{ADE}$ and $\triangle\text{ABC.}$
View full solution →ABCD is a rectangle. Points M and N are on BD such that $\text{AM}\perp\text{BD}$ and $\text{CN}\perp\text{BD}.$ Prove that $BM^2 + BN^2= DM^2+ DN^2.$
View full solution →In the given figure, AB || CD, if OA = 3x - 19, OB = x - 4, OC = x - 3 and OD = 4, find x.
A point D is on the side BC of an equilateral triangle ABC such that $\text{DC}=\frac{1}{4}\text{BC}.$ Prove that $AD^2= 13 CD^2$
View full solution →A guy wire attached to a vertical pole of height 18m is 24m long has a stake attached to the other end. How far from the base of pole should the stake be driven so that the wire will be taut?
Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay's house is 20 meter. Wen Vijay's house casts a shadow 10 m long on the ground at the same time, the tower casts a shadows 50 m long on the ground and the house of Ajay casts 20 m shadow on the ground. Based on the above information answer the following questions.
(i) The height of the tower is
(a) 20 m $\qquad$ (b) 50 m $\qquad$ (c) 100 m $\qquad$ (d) 200 m
(ii) When Vijay's house casts a shadow of 12 m , the length of the shadow of the tower is
(a) 75 m $\qquad$ (b) 50 m $\qquad$ (c) 45 m $\qquad$ (d) 60 m
(iii) The height of Ajay's house is
(a) 30 m $\qquad$ (b) 40 m $\qquad$ (c) 50 m $\qquad$ (d) 20 m
(iv) When the tower casts a shadow of 40 m , the length of the shadow of Ajay's house is
(a) 16 m $\qquad$ (b) 32 m $\qquad$ (c) 20 m $\qquad$ (d) 8 m View full solution →Observe the below given figures carefully and answer the questions:
(i) Which among the above shown figures are congruent figures?
(a) A and C $\qquad$ (b) $E$ and $F$ $\qquad$ (c) $D$ and $F$ $\qquad$ (d) $B$ and $F$
(ii) Which of the following statements is correct?
(a) All similar figures are congruent.
(b) All congruent figures are similar.
(c) The criterion for similarity and congruency is same.
(d) Similar figures have same size and shape.
(iii) If a line divides any two sides of the triangle in the same ratio, then the line is parallel to the third side. Which theorem is depicted by this statement?
(a) Pythagoras
(b) Thales Theorem
(c) Converse of Thales theorem
(d) Converse of Pythagoras theorem
(iv) Using the concept of similarity, the height of the tree is
(a) 12 ft $\qquad$ (b) 10 ft $\qquad$ (c) 15 ft $\qquad$ (d) 7 ft View full solution →View full solution →View full solution →View full solution →
(a) 20 cm $\qquad$ (b) 25 cm $\qquad$ (c) 15 cm $\qquad$ (d) 240 cm