One side of a square is $10 cm$ then its diagonal is _______ .
- A$10$
- B$20$
- ✓$10 \sqrt{2}$
- D$\frac{10}{\sqrt{2}}$
Answer: C.
View full solution →Question types
Triangles question types
158 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
158
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
45 Q→02Fill In The Blanks[1 Marks ]
36 Q→03True False[1 Marks ]
10 Q→041 Marks Question
12 Q→052 Marks Questions
24 Q→063 Marks Question
14 Q→07Match The Following.
7 Q→084 Marks Questions
10 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.
Two polygons having same number of sides are similar, if
- Atheir corresponding sides are proportional
- Btheir corresponding angles are equal
- ✓both (a) and (b)
- Dnone of these
Answer: C.
View full solution →Which of the following pairs shows similar figures?
- A
- B
- ✓
- D
Answer: C.
View full solution →If $\triangle A B C \sim \triangle P Q R$, then what are the values of $x$ and $y$ ?
- ✓$\frac{21}{4}, \frac{15}{2}$
- B$\frac{15}{2}, \frac{17}{2}$
- C$\frac{21}{2}, \frac{15}{4}$
- DNone of these
Answer: A.
View full solution →If $\triangle \text{A B C} \sim \triangle \text{P Q R}$, then $y+z$ equals
- A$2+\sqrt{3}$
- ✓$4+3 \sqrt{3}$
- C$4+\sqrt{3}$
- D$3+4 \sqrt{3}$
Answer: B.
View full solution →All ________ triangles are similar. (isosceles, equilateral)
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 →All squares are ________. (similar, congruent)
All circles are ________. (congruent, similar)
In $\triangle ABC , P$ and $Q$ are points on $AB$ and $AC$, and $PQ \| BC$. If $AP =5 cm , PB =12 cm$ and $AQ =8 cm$ then $AC =\ldots \ldots \ldots . . cm .(17.2,27.2,27.5)$
View full solution →Ratio of the areas of the similar triangle is the same as the ratio of the square of the corresponding sides.
In $\triangle ABC , \angle B =90^{\circ} AB =8 cm$ and $BC =15 cm$ then perimeter of $\triangle ABC$ is $40 cm$.
View full solution →Two chords intersects each other in inner part of circle then $\frac{ OA }{ OB }=\frac{ OC }{ OD }$.
View full solution →If in $\triangle ABC AB =5 cm , BC =12 cm$ and $AC =15 cm$ then $\triangle ABC$ is an obtuse angle triangle.
View full solution →Any two square are similar.
In the figure, altitudes $AD$ and $CE$ of $\triangle$$ABC$ intersect each other at the point $P$. Show that: $\vartriangle PDC \sim \vartriangle BEC$ 
View full solution →In the figure, altitudes $AD$ and $CE$ of $\triangle$$ABC$ intersect each other at the point $P$. Show that: $\vartriangle AEP \sim \vartriangle ADB$
View full solution →In the figure, altitudes $AD$ and $CE$ of $\triangle$$ABC$ intersect each other at the point $P$. Show that: $\vartriangle ABD \sim \vartriangle CBE$
View full solution →In the figure, altitudes $AD$ and $CE$ of $\triangle$$ABC$ intersect each other at the point $P.$ Show that: $\vartriangle AEP \sim \vartriangle CDP$
View full solution →State the pair of triangles in the figure below are similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:
If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
In the figure, $ABC$ and $AMP$ are two right triangles, right angled at $B$ and $M$ respectively. Prove that:
View full solution →- $\triangle ABC \sim \triangle AMP$
- $\frac{{CA}}{{PA}} = \frac{{BC}}{{MP}}$
$E$ is a point on side $AD$ produced of a parallelogram $ABCD$ and $BE$ intersects $CD$ at $F$. Prove that $\Delta A B E \sim \Delta C F B.$
View full solution →In the figure, if $\triangle$$ABE$ $\cong$ $\triangle$$ACD$. Show that $\triangle$$ADE$ ~ $\triangle$$ABC$
View full solution →$S$ and $T$ are points on sides $PR$ and $QR$ of $\triangle PQR$ such that $\angle P = \angle R T S$. Show that $\triangle R P Q \sim \triangle R T S$.
View full solution →If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar:
In Figure, $\frac{{QR}}{{QS}} = \frac{{QT}}{{PR}}$ and $\angle 1 = \angle 2.$ Show that $\triangle PQS \sim \triangle TQR .$
View full solution →Sides $AB$ and $BC$ and median $AD$ of a triangle $ABC$ are respectively proportional to sides $PQ$ and $QR$ and median $PM$ of $\triangle PQR ($see figure$).$ Show that $\triangle A B C \sim \triangle P Q R$.
View full solution →In the figure, $E$ is the point on side $CB$ produced on an isosceles triangle $ABC$ with $AB = AC.$ If $AD \bot BC$ and $EF \bot AC,$ prove that $\triangle ABD \sim \triangle ECF.$
View full solution →$ABCD$ is a trapezium in which $AB || DC$ and its diagonals intersect each other at the point $O.$ Show that $\frac{{AO}}{{BO}} = \frac{{CO}}{{DO}}$.
View full solution →| A | B |
| Q.1. In an equilateral triangle, the length of its median is $\sqrt{3}$. The length of its side is ..... | (a) 8, 24, 26 |
| Q.2. If the measures of the sides of a triangle is ....... then the triangle is not a right angle triangle. | (b) $2 \sqrt{3}$ |
| (c) 2 |
| A | B |
| Q.1. $\triangle ABC \sim \triangle PQR$, Area of $\triangle ABC :$ Area of $\triangle PQR = BC ^2: \ldots \ldots$ | (a) acute angle |
| Q.2. If the sum of the square of two smaller sides in a triangle is smaller than the square of the third side, then the triangle is ......... triangle. | (b) $QR ^2$ |
| (c) obtuse angle |
| A | B |
| Q.1. If in two triangles, the corresponding ......... sides are in proportion then the triangles are similar | (a) Three |
| Q.2. If the corresponding sides of two triangles are in proportion then their corresponding angles are ......... | (b) Congruent |
| (c) Two |
| A | B |
| Q.1. For correspondence of two triangles at least ...... pair of angle must equal then the two triangles are similar. | (a) One |
| Q.2. For $\triangle ABC$ and $\triangle PQR \frac{ AB }{ PQ }=\frac{ AC }{ PR }$ and then the triangles are similar. | (b) Two |
| (c) $\angle A =\angle P$ |
| A | B |
Q.1. In $\triangle XYZ$ and $\triangle PQR$ the correspondence $XYZ \leftrightarrow QPR$ is similar which statement is not true? | (a) AAA |
| Q.2. ......... condition is not apply for two triangles become similar. | (b) ASS |
| (a) $\frac{ XZ }{ PQ }=\frac{ YZ }{ PR }$ |
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR,$ respectively where $\triangle ABC \sim \triangle PQR,$ Prove that $\frac{{AB}}{{PQ}} = \frac{{AD}}{{PM}}$
View full solution →A vertical pole of length $6\ m$ casts a shadow $4\ m$ long on the ground and at the same time a tower casts a shadow $28\ m$ long. Find the height of the tower.
View full solution →Sides $AB$ and $AC$ and median $AD$ of a triangle $ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of another triangle $PQR.$ Show that $\Delta A B C \sim \Delta P Q R$.
View full solution →$CD$ and $GH$ are respectively the bisectors of $\angle ACB$ and $\angle EGF$ such that $D$ and $H$ lie on sides $AB$ and $FE$ of $\triangle ABC$ and $\triangle EFG$ respectively. If $\triangle ABC \sim\triangle FEG,$ show that:
View full solution →- $\frac{C D}{G H}=\frac{A C}{F G}$
- $\triangle DCB \sim\triangle HGE$
- $\triangle DCA \sim\triangle HGF$
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