In triangle P Q R , P Q = 4 3 c e n t i m e t r e s , ∠ P = ∠ Q = 30 ° . Draw the triangle.

In triangle P Q R , P Q = 4 3 c e n t i m e t r e s , ∠ P = ∠ Q = 30 ° . We have to draw the triangle. Steps to be followed: ( i ) Draw a line segment P Q = 4 3 c m . ( i i ) At P, draw a ray making an angle of 30 ° ( i i i ) At Q, draw another ray making an angle of 30 ° which intersects the first ray at R . ∆ P Q R is the required triangle.

Construct Δ P Q R if P Q = 5 c m , m ∠ P Q R = 105 o and m ∠ Q R P = 40 o .

In order to construct the required triangle, we need the measure of ∠ R P Q . We make use of the angle sum property of a triangle to find ∠ R P Q . ∠ P Q R + ∠ P R Q + ∠ R P Q = 180 o 105 o + 40 o + ∠ R P Q = 180 o 145 o + ∠ R P Q = 180 o ∠ R P Q = 180 o - 145 o = 35 o The rough sketch of the required triangle is as shown below: The following are the steps of construction: (i) Since, we have considered P Q to be the base of the triangle, draw a line segment P Q of length 5 c m . (ii) Since we have an angle of 35 o at point P , construct a ray P X such that it makes an angle of 35 o with point P . (iii) Since we have an angle of 105 o at Q , construct a ray Q Y such that it makes an angle of 105 o at Q . (iv) Extend the rays such that they intersect at point. Name this point of intersection as R . Hence, P Q R is the required triangle.

EASY

Earn 100

Draw a right triangle with hypotenuse of length $5 cm$ and one side of length $4 cm$ .

Important Questions on Geometrical Constructions

HARD

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

∆ A B C, A B = 5

centimetres,

∠ A = 65 °, ∠ B = 55 °

. Draw the triangle

A B C

and draw the incircle. Measure the radius of the incircle.

EASY

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

In triangle $P Q R, P Q = 4 \sqrt{3} c e n t i m e t r e s, ∠ P = ∠ Q = 30 °$ . Draw the triangle.

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Using ruler and compass construct a triangle $A B C$ where $A B = 3 cm, B C = 4 cm$ and $∠ A B C = 90 °$ . Hence construct a circle circumscribing the triangle $A B C$ . Measure and write down the radius of the circle.

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct a right triangle having hypotenuse of length

5.6 cm

and one of whose acute angles measures

30 °

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct a

△ A B C

in which

B C = 3.6 cm, A B = 5 cm

and

A C = 5.4 cm

. Draw the perpendicular bisector of the side $B C$ .

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct a right-angled triangle whose hypotenuse is

6 c m

long and one of the legs is

4 c m

long.

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct

Δ P Q R

P Q = 5 c m, m ∠ P Q R = 105^{o}

and

m ∠ Q R P = 40^{o} .

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct a

△ A B C

in which

A B = A C = 5.2 cm

and

∠ A = 120 °

. Draw

A D ⊥ B C

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct an isosceles triangle in which the lengths of each of its equal sides is

6.5 c m

and the angle between them is

110^{o} .

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct

Δ X Y Z

in which

X Y = 4.5 c m, Y Z = 5 c m

and

Z X = 6 c m .

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct an equilateral triangle of side

5.5 c m

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct an equilateral triangle each of whose sides measures

6.2 cm

. Measure each of its angles.

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct an isosceles right-angled triangle

A B C,

where,

m ∠ A C B = 90^{o}

and

A C = 6 c m .

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct a

△ A B C

in which

A B = A C = 4.8 cm

and

B C = 5.3 cm

. Measure

∠ B

and

∠ C

. Draw

A D ⊥ B C

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct

Δ A B C

such that

A B = 2.5 c m, B C = 6 c m

and

A C = 6.5 c m

. Measure

∠ B

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct

Δ A B C,

given

m ∠ A = 60^{o}, m ∠ B = 30^{o}

and

A B = 5.8 c m .

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Draw

Δ P Q R

with

P Q = 4 c m, Q R = 3.5 c m

and

P R = 4 c m

. What type of triangle is this?

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Examine whether you can construct

Δ D E F

such that

E F = 7.2 c m, m ∠ E = 110^{o}

and

m ∠ F = 80^{o}

. Justify your answer.

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Examine whether you can construct

Δ D E F

such that

E F = 7.2 c m, m ∠ E = 110^{o}

and

m ∠ F = 80^{o}

. Justify your answer.

MEDIUM

Mathematics>Geometry>Geometrical Constructions>Construction of Triangles

Construct

Δ D E F

such that

D E = 5 c m, D F = 3 c m

and

m ∠ E D F = 90^{o}

Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm.

Important Questions on Geometrical Constructions

Learn and Prepare for any exam you want !

Draw a right triangle with hypotenuse of length $5 cm$ and one side of length $4 cm$ .