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:
- A
$18cm$.
- B
$20cm$.
- C
$12cm$.
- ✓
$15cm$.
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:
- A
$7.5cm$.
- ✓
$15cm$.
- C
$22.5cm$.
- D
$30cm$.
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 $DEF$ and $ABC$ 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 $\text{Area}(\triangle\text{ADE}):\text{Area}(\Box\text{BCED})=$
- A
$3 : 4.$
- ✓
$9 : 16.$
- C
$3 : 5.$
- D
$9 : 25.$
Answer: B.
View full solution →Fill in the blanks using the correct word given in brackets:
Two triangles are similar, if their corresponding angles are .......... (proportional, equal).
Fill in the blanks using the correct word given in brackets:
Two polygons of the same number of sides are similar,
if $(a)$ their corresponding angles are and $(b)$ their corresponding sides are ........... (equal, proportional).
View full solution → Fill in the blanks using the correct word given in brackets:
All circles are ......... (congruent, similar).
Fill in the blanks using the correct word given in brackets:
All squares are ........ (similar, congruent).
Fill in the blanks using the correct word given in brackets:
All .......... triangles are similar (isosceles, equilateral).
Write the truth value $(T/F)$ of the following statements:
Two polygons are similar, if their corresponding sides are proportional.
View full solution →Write the truth value $(T/F)$ of the following statements:
Any two congruent figures are similar.
View full solution →Write the truth value $(T/F)$ of the following statements:
Any two similar figures are congruent.
View full solution →Write the truth value $(T/F)$ of each of the following statements:
Two triangles are similar, if their corresponding sides are proportional.
View full solution →Write the truth value $(T/F)$ of the following statements:
Two polygons are similar, if their corresponding angles are proportional.
View full solution → State AAA similarity criterion.
In the adjoining figure, find $AC.$
View full solution →In the given figure, $\triangle\text{AHK}$ is similar to $\triangle\text{ABC}.$ If $AK = 10\ cm, BC = 3.5\ cm$ and $HK = 7\ cm,$ 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 $BC = 2.3\ cm,$ 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 $AD = 4\ cm, DB = 4.5\ cm$ and $AE = 8\ cm,$ find $AC.$
View full solution →In the given figure, $LM = LN = 46^\circ .$ Express $x$ in terms of $a, b$ and $c$ where $a, b, c$ are lengths of $LM, MN$ and $NK$ respectively.
View full solution →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 $AB = 6\ cm,$ find $AD.$
View full solution →In $\triangle\text{ABC and }\triangle\text{DEF},$ it is being given that: $AB = 5\ cm, BC = 4\ cm$ and $CA = 4.2\ cm; DE = 10\ cm, EF = 8\ cm$ and $FD = 8.4\ cm.$ 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 $x.$
View full solution →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 $18\ m$ is $24\ m$ 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?
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