### Introduction to similarity - class-IX

Description: introduction to similarity | |

Number of Questions: 73 | |

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Tags: similar triangles exploring geometrical figures similarity in geometrical shapes properties of parallel lines and their transversal triangles geometry maths pythagoras' theorem and similar shapes similarity congruence |

Two polygons of different number of side ...... be similar.

If the corresponding angles are equal then the two figures having samenumber of sides are said to be

If the same photograph is printed in different sizes , we say it is

Two quadrilaterals, a square and a rectangle are not similar as they ......... in shape as well as size.

Ratio of two corresponding sides of two similar triangles is $4:9$. Then ratio of their area is ___.

$\triangle PQR \sim \triangle XYZ, \dfrac{XY}{PQ}=\dfrac{3}{2}$ then $\dfrac{Area\ of\ \triangle PQR}{Area\ of\ \triangle XYZ}=$____.

ABCD is a tetrahedron and O is any point. If the lines joining O to the vertices meet the opposite at P, Q, R and S, then $\frac{OP}{AP}+\frac{OQ}{BQ}+\frac{OR}{CR}+\frac{OS}{DS}=2$.

It is given that $\Delta ABC \sim \Delta PQR$ with $\dfrac{BC}{QR} = \dfrac{1}{3}$. Then $\dfrac{ar (\Delta PQR)}{ar (\Delta ABC)}$ is equal to

$CM$ and $RN$ are respectively the medians of $\triangle {ABC}$ and $\triangle{PQR}$. If $\triangle {ABC}\sim \triangle{PQR}$, then

$\cfrac{CM}{RN}=\cfrac{AB}{PQ}$

In a square $ABCD$, the bisector of the angle $BAC$ cut $BD$ at $X$ and $BC$ at $Y$ then triangles $ACY, ABX$ are similar.

Assume that, $\Delta RST \sim \Delta XYZ$. Complete the following statement.

Consider the following statements:

(1) If three sides of triangle are equal to three sides of another triangle, then the triangles are congruent.

(2) If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.

If in trianges $ABC$ and $DEF$, $\cfrac{AB}{DE}=\cfrac{BC}{FD}$, then they will be similar, when:

In $\triangle PQR,$ $PQ=4$ cm, $QR=3$ cm, and $RP=3.5$ cm. $\triangle DEF$ is similar to $\triangle PQR.$ If $EF=9$ cm, then what is the perimeter of $\triangle DEF: ?$

The perimeter of two similar triangles are $24$ cm and $16$ cm, respectively. If one side of the first triangle is $10$ cm, then the corresponding side of the second triangle is

In a $\triangle ABC$, $BC=AB$ and $\angle B={ 80 }^{ 0 }$. Then $\angle A$ is equal to?

The area of two similar triangles $\displaystyle \Delta ABC$ and $\displaystyle \Delta DEF$ are 144 $\displaystyle cm^{2}$ and 81 $\displaystyle cm^{2}$ respectively If the longest side of larger $\displaystyle \Delta ABC$ be 36 cm then the longest side of the smaller triangle $\displaystyle \Delta DEF$ is

The perimeters of two similar triangles are $25\;cm$ and $15\;cm$ respectively. If one side of first triangle is $9\;cm$, then the corresponding side of the other triangle is

If area $(\Delta ABC)=36 cm^2, area (\Delta DEF)=64 cm^2$ and $DE=6.4 cm$. Find AB if $\Delta ABC\sim \Delta DEF$

If the areas of two similar triangles are equal then the triangles :

Sides of two similar triangles are in the ratio of $5 : 11$ then ratio of their areas is

Sides of two similar triangles are in the ratio of $4 : 9$ then area of these triangles are in the ratio

Similarity is represented by :

When the ratios of the lengths of their corresponding sides are equal, then the two figures are:

Two triangles are $ABC$ and $PQR$ are similar, then symbolically it is represented as:

All congruent figures are similar but the similar figures are not congruent.Is this statement true or false?

A tree of height 24m standing in the middle of the road casts a shadow ofheight 16m. If at the same time a nearby pole of 48 m casts a shadow , what would the height of the shadow be?

There were three circular tracks made in a park having the same middle point but their radii was different. These tracks will be called

All ......... triangles are similar.

Anna went to the market to buy some boxes to store things. She was surprised to find boxes one inside the other. They were ....... boxes.

If two triangles are ____ they are similar.

When one acute angle of a triangle is equal to one acute angle of other triangle, and the triangles are right angles, do you think the triangles are similar?

If corresponding angles of two triangles are equal, then they are known as

If the angles of one triangle $ABC$ are congruent with the corresponding angles of triangle $DEF$, which of the following is/are true?

Which of the following is true?

If the area of two similar triangles are equal, then they are

Two polygons of the same number of sides are similar if all the corresponding interior angles are:

Triangle is equilateral with side$A$, perimeter $P$, area $K$ and circumradius $R$ (radius of the circumscribed circle). Triangle is equilateral with side $a$, perimeter $p$, area $k$, and circumradius $r$. If $A$ is different from $a$, then

If in two triangles, corresponding angles are _______ and their corresponding sides are in the ______ratio and hence the two triangles are similar.

Which among the following is/are not correct ?

The ratio of the areas of two similar triangles is equal to the

In two similar triangles ABC and PQR, if their corresponding altitudes AD and Ps are in the ratio 4:9, find the ratio of the areas of $\triangle ABC$ and $\triangle PQR$.

If $\triangle ABC$ is similar to $\triangle DEF$ such that BC=3 cm, EF=4 cm and area of $\triangle ABC=54 {cm}^{2}$. Determine the area of $\triangle DEF$.

Two $\triangle sABC $ and DEF are similar. If $ar(DEF)= 243\ cm^2, ar(ABC)=108\ cm^2$ and $BC= 6\ cm$. Find $EF$.

$\Delta ABC$ and $\Delta DEF$ are similar and $\angle A=40^\mathring \ ,\angle E+\angle F=$

STATEMENT - 1 : If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.

STATEMENT - 2 : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

If $\triangle ABC $ and $BDE$ are similar triangles such that $2AB = DE$ and $BC= 8$ cm, then $EF$ is

Is the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians?

The areas of two similar triangles $\triangle{ABC}$ and $\triangle{DEF}$ are $144\ cm^{2}$ and $81\ cm^{2}$ respectively. If the longest side of larger $\triangle{ABC}$ be $36\ cm$, then, the largest side of the similar triangle $\triangle{DEF}$ is

The correspondence $ABC\rightarrow PQR$ is a similarity in $\Delta ABC$ and $\Delta PQR$. If the perimeter of $\Delta ABC$ is $24$ and the perimeter of $\Delta PQR$ is $40$, then $AB=PQ=$

$\triangle XYZ \sim \triangle DEF$ for the corresponding $XYZ-EFD$ if $mLX:mLY:mLz=2:3:5$ then in $\triangle DEF$_____ is a right angle.

The ratio of the angles in $\triangle ABC$ is $2 : 3 : 4$. Which one of the following triangles is similar to $\triangle ABC ?$

The length of the sides of $\triangle DEF$ are $4,6,8$ $\triangle DEF \sim \triangle PQR$ for correspondence $DEF \leftrightarrow QPR$ if the perimeter of $\triangle PQR=36$, then the length of the smallest side of $\triangle PQR$ is_____

If $A={30}^{\circ},\,a=100,\,c=100\sqrt{2}$, find the number of triangles that can be formed.

In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that $\Delta\,BPC$ is similar to $\Delta\,ABC$. Also, find the length of BP.

In the given figure, $DE$ is parallel to $BC$ and the ratio of the areas of $\triangle ADE$ and trapezium $BDEC$ is $4:5.$ What is $DE : BC: ?$

If in $\triangle $s $ABC$ and $DEF,$ $\angle A=\angle E=37^{\circ}, AB:ED=AC:EF$ and $\angle F=69^{\circ},$ then what is the value of $\angle B: ?$

If two triangles are similar then, ratio of corresponding sides are:

Two equilateral triangles with side $4 \ cm$ and $6 \ cm$ are _____ triangles.

In $\triangle ABC \sim \triangle DEF$ such that $AB = 1.2\ cm$ and $DE = 1.4\ cm$. Find the ratio of areas of $\triangle ABC$ and $\triangle DEF$.

The perimeter of two similar triangle are $30\ cm$ and $20\ cm$. If one side of first triangle is $12\ cm$ determine the corresponding side of second triangle.

Which of the following is/are the property of similar figures?

$\displaystyle \Delta ABC$ and $\displaystyle \Delta DEF$ are two similar triangles such that $\displaystyle \angle A={ 45 }^{ \circ },\angle E={ 56 }^{ \circ }$, then $\displaystyle \angle C$ =___.

If triangle $ABC$ has vertices as $(2, 1), (6, 1), (4, 7)$ and triangle $DEF$, with vertices as $(3, -1), (p,q), (5, -1),$ where $q<-1$, is similar to triangle $ABC$, then $(p,q)$ is equivalent to:

If a triangle with side lengths as $5, 12$, and $15$ cm is similar to a triangle which has longer side length as $24$ cm, then the perimeter of the other triangle is:

The perimeter of two similar triangles $\triangle ABC$ and $\triangle DEF$ are $36$ cm and $24$ cm respectively. If $DE=10 $ cm, then $AB$ is :

In $\Delta ABC$, DE is || to BC, meeting AB and AC at D and E. If AD = 3 cm, DB = 2 cm and AE = 2.7 cm, then AC is equal to:

The sides of a triangle are $5$ cm, $6$ cm and $7$ cm. One more triangle is formed by joining the midpoints of the sides. The perimeter of the second triangle is:

Point L, M and N lie on the sides AB, BC and CA of the triangle ABC such that $\ell (AL) : \ell (LB) = \ell (BM) : \ell (MC) = \ell (CN) : \ell (NA) = m : n$, then the areas of the triangles LMN and ABC are in the ratio

A man of height 1.8 metre is moving away from a lamp post at the rate of 1.2 m/sec . If the height of the lamp post be 4.5 metre , then the rate at which the shadow of the man is lengthening is