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Two isosceles triangles are similar, if an angle of one is congruent to the corresponding angle of the other.

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Important Questions on Triangles

EASY

Mathematics>Geometry>Triangles>Similarity of Triangles

△ A B C ~ △ P Q R

\frac{a r (A B C)}{a r (P Q R)} = \frac{9}{4}

A C = 12 cm, A B = 18 cm

and

B C = 15 cm

then

P R

is equal to _____.

MEDIUM

Mathematics>Geometry>Triangles>Similarity of Triangles

Let

△ ABC ~ △ RPQ

and

\frac{ar △ ABC}{ar △ RPQ} = \frac{1}{4}

. If PQ

= 4

cm,QR

= 6

cm and PR

= 7

cm, then AC is equal to_____.

MEDIUM

Mathematics>Geometry>Triangles>Similarity of Triangles

∆ ABC, D

and

E

are the points on sides

AB

and

BC

respectively such that

DE ∥ AC

. If

AD : DB = 5 : 3

, then what is the ratio of the area of

∆ BDE

to that of the trapezium

ACED

MEDIUM

Mathematics>Geometry>Triangles>Similarity of Triangles

Suppose

B C

is a given line segment in the plane and

T

is a scalene triangle. The number of points

A

in the plane such that the triangle with vertices

A, B, C

(in same order) is similar to triangle

T

HARD

Mathematics>Geometry>Triangles>Similarity of Triangles

In a quadrilateral

A B C D,

which is not a trapezium, it is known that

∠ D A B = ∠ A B C = 60 ° .

Moreover,

∠ C A B = ∠ C B D .

Then

EASY

Mathematics>Geometry>Triangles>Similarity of Triangles

∆ A B C, D

is a point on side

B C

such that

∠ ADC = ∠ BAC

. If

C A = 12 cm, C B = 8 cm

then

C D

is equal to:

EASY

Mathematics>Geometry>Triangles>Similarity of Triangles

The perimeter of similar triangles

ABC

and

PQR

are

78 cm

and

46.8 cm

, respectively. If

PQ = 11.7

, then the length of

AB

is______.

MEDIUM

Mathematics>Geometry>Triangles>Similarity of Triangles

In the given figure $A B = 9 c m, P A = 7.5 c m & P C = 5 c m$ .

Chord $A D & B C$ intersect at $P$ .

Prove that $∆ P A B ~ ∆ P C D$

Question Image

HARD

Mathematics>Geometry>Triangles>Similarity of Triangles

In a

△

ABC, MN

∥

BC, the area of quadrilateral MBCN is equal to

130 {cm}^{2}

. If AN

:

NC is

4 : 5

, then the area of

△

AMN is:

EASY

Mathematics>Geometry>Triangles>Similarity of Triangles

∆ P Q R, P Q = 24 c m

and

∠ Q = 58 °

S

and

T

are the points on the side

P Q

and

P R

, respectively such that

∠ S T R = 122 °

. If

P S = 14 c m & P T = 12 c m

, then the length of

R T

is:

HARD

Mathematics>Geometry>Triangles>Similarity of Triangles

Let $A B C$ be a triangle and $M$ be a point on side $A C$ closer to vertex $C$ than $A$ . Let $N$ be a point on side $A B$ such that $M N$ is parallel to $B C$ and let $P$ be a point on side $B C$ such that $M P$ is parallel to $A B$ . If the area of the quadrilateral $B N M P$ is equal to $\frac{5}{18}$ of the area of $Δ A B C$ , then the ratio $A M / M C$ equals

MEDIUM

Mathematics>Geometry>Triangles>Similarity of Triangles

△ A B C ~ △ R Q P

and

A B = 4 c m, B C = 6 c m

and

A C = 5 c m

. If

a r (△ A B C) : a r (△ P Q R) = 9 : 4

, then

P Q

is equal to:

HARD

Mathematics>Geometry>Triangles>Similarity of Triangles

Let

A B C

be an equilateral triangle with side length

10 .

A square

P Q R S

is inscribed in it, with

P

A B . Q, R

B C

and

S

A C .

If the area of the square

P Q R S

m + n \sqrt{k}

where

m, n

are integers and

k

is a prime number then determine the value of

\sqrt{\frac{m + n}{k^{2}}}

HARD

Mathematics>Geometry>Triangles>Similarity of Triangles

Let

A B C

be a triangle with sides

51, 52, 53 .

Let

Ω

denote the incircle of

∆ A B C .

Draw tangents to

Ω

which are parallel to the sides of

A B C .

Let

r_{1}, r_{2}, r_{3}

be the inradii of the three corner triangles so formed. Find the largest integer that does not exceed

r_{1} + r_{2} + r_{3} .

HARD

Mathematics>Geometry>Triangles>Similarity of Triangles

Let

A B C

be a triangle with

∠ C = 90 ° .

Draw

C D

perpendicular to

A B

. Choose points

M

and

N

on sides

A C

and

B C

respectively such that

D M

is parallel to

B C

and

D N

is parallel to

A C

. If

D M = 5, D N = 4

, then

A C

and

B C

are respectively equal to

MEDIUM

Mathematics>Geometry>Triangles>Similarity of Triangles

Define similar triangles.

MEDIUM

Mathematics>Geometry>Triangles>Similarity of Triangles

In the given figure $A B = 9 cm$ , $P A = 7.5 cm$ and $P C = 5 cm$ . Chords $A D$ and $B C$ intersect at $P$ . Find the length of $C D .$

Question Image

EASY

Mathematics>Geometry>Triangles>Similarity of Triangles

In the given figure, if $D E ∥ B C, A D = 2.5 c m, D B = 3.5 c m$ and $E C = 4.2 c m$ , then the measure of $A C$ is:

Question Image

EASY

Mathematics>Geometry>Triangles>Similarity of Triangles

Consider the following figure shown below and choose which of the following equation is CORRECT about the similarity of both triangles?

Question Image

HARD

Mathematics>Geometry>Triangles>Similarity of Triangles

Let

C_{1}, C_{2}

be two circles touching each other externally at the point

A

and let

A B

be the diameter of circle

C_{1}

. Draw a secant

B A_{3}

to circle

C_{2}

, intersecting circle

C_{1}

at a point

A_{1} (\neq A),

and circle

C_{2}

at points

A_{2}

and

A_{3}

. If

B A_{1} = 2, B A_{2} = 3

and

B A_{3} = 4

then the radii of circles

C_{1}

and

C_{2}

are respectively

Two isosceles triangles are similar, if an angle of one is congruent to the corresponding angle of the other.

Important Questions on Triangles

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