EASY

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If$\angle$ABC ≌$\angle$DEF, what is the measure of $\angle$DEF ?

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Important Questions on Congruence of Triangles

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

The measures of the sides of a triangle are 7, 8 and 9 cm. Find the length of the largest side of a similar triangle whose shortest side is 35 cm.

(A) 55 cm

(B) 40 cm

(D) 50 cm

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

The side of an equilateral triangle is

10 c m

. Find its area (in

c m^{2}

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

∆

D E F

is right angled at E. If m

∠ F = 30^{o}

, then find the value of

[\cos D - \frac{1}{\sqrt{2}}]

MEDIUM

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

For a Right angled triangle, two connected sides are 1.5 & 2 cm. Find the area of circumcircle?

MEDIUM

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence 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

MEDIUM

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

X, Y and Z are the midpoints of the sides of ∆PQR. If the perimeter of ∆XYZ is 32 units, find the perimeter of ∆PQR.

(A) 128 units

(B) 64 units

(D) 160 units

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

The circle of radius

4 c m

and centre

O

has a tangent

P R

. If

∠ P O R = 90^{o}

and

O R = 7 c m

and

O P = 24 c m

. Calculate the length (in

c m

.) of

P R

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

In the triangle

A B C

∠ B A C = 50 °

and the bisectors of

∠ A B C

and

∠ A C B

meets at

P

. What is the value (in degrees) of

∠ B P C

MEDIUM

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

∆ A B D

C

is the midpoint of

B D

. If

A B

= 10

cm, AD

= 12

cm and

A C

= 9

cm, then

B D = ?

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

The area of an equilateral triangle is

18 \sqrt{3}

sq. units. Find the value of the side (in units) of the triangle.

MEDIUM

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

In an equilateral triangle

A B C, D, E, F

are the mid-points of

A B, B C,

and

A C

respectively. The quadrilateral

B E F D

is a _____.

HARD

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence 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

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

The angles of a triangle are in the ratio of 1 : 2 : 3. What is the measure of the smallest angle (in degrees)?

HARD

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

A very tall tree breaks from the middle due to storm. The broken part of the tree did not separate from the tree and the top of the tree touched the ground at a distance of

12

metre from the base of the tree. If the tree broke at the height of

37

metre from the ground, then what is the length of the broken portion of the tree in metres?

MEDIUM

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence 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:

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

The perimeters of two similar triangles

A B C

and

P Q R

are

78 cm

and

46.8 cm

respectively. If

P Q

=

11.7

, then the length of

A B

is:

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

△ P Q R

∠ R = 54 °

, the perpendicular bisector of

P Q

S

meets

Q R

T

. If

∠ T P R = 46 °

, then what is the value(in degrees) of

∠ P Q R

EASY

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence of Triangles

△ A B C,

the measure of angle

∠ A B C

90 °

. If

tan A = \frac{12}{5},

and

A B = 1 c m

, then what is the length (in

c m

) of side

B C ?

HARD

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence 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

HARD

Mathematics>Geometry>Congruence of Triangles>Introduction to Congruence 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

If$\angle$ABC ≌$\angle$DEF, what is the measure of $\angle$DEF ?

Important Questions on Congruence of Triangles

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