Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board chapter 4 - Geometry [Latest edition]

In the figure, AB is parallel to CD, find x

In the figure, AB is parallel to CD, find x

In the figure, AB is parallel to CD, find x

The angles of a triangle are in the ratio 1 : 2 : 3, find the measure of each angle of the triangle

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

ΔABC and ΔDEF are two triangles in which AB = DF, ∠ACB = 70°, ∠ABC = 60°, ∠DEF = 70° and ∠EDF = 60°. Prove that the triangles are congruent

Find all the three angles of the ΔABC

The angles of a quadrilateral are in the ratio 2 : 4 : 5 : 7. Find all the angles

In a quadrilateral ABCD, ∠A = 72° and ∠C is the supplementary of ∠A. The other two angles are 2x – 10 and x + 4. Find the value of x and the measure of all the angles

ABCD is a rectangle whose diagonals AC and BD intersect at O. If ∠OAB = 46°, find ∠OBC

The lengths of the diagonals of a Rhombus are 12 cm and 16 cm. Find the side of the rhombus

Show that the bisectors of angles of a parallelogram form a rectangle

If a triangle and a parallelogram lie on the same base and between the same parallels, then prove that the area of the triangle is equal to half of the area of parallelogram

Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between b and c

Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between d and e

Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between d and f

Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between c and f

In the given figure, ∠A = 64°, ∠ABC = 58°. If BO and CO are the bisectors of ∠ABC and ∠ACB respectively of ΔABC, find x° and y°

In the given Figure, if AB = 2, BC = 6, AE = 6, BF = 8, CE = 7, and CF = 7, compute the ratio of the area of quadrilateral ABDE to the area of ΔCDF. (Use congruent property of triangles)

In the Figure, ABCD is a rectangle and EFGH is a parallelogram. Using the measurements given in the figure, what is the length d of the segment that is perpendicular to `bar("HE")` and `bar("FG")`?

In parallelogram ABCD of the accompanying diagram, line DP is drawn bisecting BC at N and meeting AB (extended) at P. From vertex C, line CQ is drawn bisecting side AD at M and meeting AB (extended) at Q. Lines DP and CQ meet at O. Show that the area of triangle QPO is `9/8` of the area of the parallelogram ABCD

The diameter of the circle is 52 cm and the length of one of its chord is 20 cm. Find the distance of the chord from the centre

The chord of length 30 cm is drawn at the distance of 8 cm from the centre of the circle. Find the radius of the circle

Find the length of the chord AC where AB and CD are the two diameters perpendicular to each other of a circle with radius `4sqrt(2)` cm and also find ∠OAC and ∠OCA

A chord is 12 cm away from the centre of the circle of radius 15 cm. Find the length of the chord

In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords?

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord

Find the value of x° in the following figure:

Find the value of x° in the following figure:

Find the value of x° in the following figure:

Find the value of x° in the following figure:

Find the value of x° in the following figure:

In the given figure, ∠CAB = 25°, find ∠BDC, ∠DBA and ∠COB

Find the value of x in the given figure.

In the given figure, AC is the diameter of the circle with centre O. If ∠ADE = 30°, ∠DAC = 35° and ∠CAB = 40°. Find ∠ACD

In the given figure, AC is the diameter of the circle with centre O. If ∠ADE = 30°, ∠DAC = 35° and ∠CAB = 40°. Find ∠ACB

In the given figure, AC is the diameter of the circle with centre O. If ∠ADE = 30°, ∠DAC = 35° and ∠CAB = 40°. Find ∠DAE

Find all the angles of the given cyclic quadrilateral ABCD in the figure.

In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that ∠DBC = 40° and ∠BAC = 60° find ∠CAD

In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that ∠DBC = 40° and ∠BAC = 60° find ∠BCD

In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8 cm and CD = 6 cm. If OM ⊥ AB and OL ⊥ CD distance between LM is 7cm. Find the radius of the circle?

The arch of a bridge has dimensions as shown, where the arch measure 2m at its highest point and its width is 6m. What is the radius of the circle that contains the arch?

In figure ∠ABC = 120°, where A, B and C are points on the circle with centre O. Find ∠OAC?

A school wants to conduct tree plantation programme. For this a teacher allotted a circle of radius 6 m ground to nineth standard students for planting sapplings. Four students plant trees at the points A, B, C and D as shown in figure. Here AB = 8 m, CD = 10 m and AB ⊥ CD. If another student places a flower pot at the point P, the intersection of AB and CD, then find the distance from the centre to P.

In the given figure, ∠POQ = 100° and ∠PQR° = 30°, then find ∠RPO

Construct the ΔLMN such that LM = 7.5 cm, MN = 5 cm and LN = 8 cm. Locate its centroid

Draw and locate the centroid of the triangle ABC where right angle at A, AB = 4 cm and AC = 3 cm

Draw the ΔABC, where AB = 6 cm, ∠B = 110° and AC = 9 cm and construct the centroid

Construct the ΔPQR such that PQ = 5 cm, PR = 6 cm and ∠QPR = 60° and locate its centroid

Draw ΔPQR with sides PQ = 7 cm, QR = 8 cm and PR = 5 cm and construct its Orthocentre

Draw an equilateral triangle of sides 6.5 cm and locate its Orthocentre

Draw ΔABC, where AB = 6 cm, ∠B = 110° and BC = 5 cm and construct its Orthocentre

Draw and locate the Orthocentre of a right triangle PQR where PQ = 4.5 cm, QR = 6 cm and PR = 7.5 cm

Draw a triangle ABC, where AB = 8 cm, BC = 6 cm and ∠B = 70° and locate its circumcentre and draw the circumcircle

Construct the right triangle PQR whose perpendicular sides are 4.5 cm and 6 cm. Also locate its circumcentre and draw circumcircle

Construct ΔABC with AB = 5 cm ∠B = 100° and BC = 6 cm. Also locate its circumcentre draw circumcircle

Construct an isosceles triangle PQR where PQ = PR and ∠Q = 50°, QR = 7 cm. Also draw its circumcircle.

Draw an equilateral triangle of side 6.5 cm and locate its incentre. Also draw the incircle

Draw a right triangle whose hypotenuse is 10 cm and one of the legs is 8 cm. Locate its incentre and also draw the incircle

Draw ΔABC given AB = 9 cm, ∠CAB = 115° and ∠ABC = 40°. Locate its incentre and also draw the incircle.

Construct ΔABC in which AB = BC = 6 cm and ∠B = 80°. Locate its incentre and draw the incircle

The exterior angle of a triangle is equal to the sum of two

In the quadrilateral ABCD, AB = BC and AD = DC Measure of ∠BCD is

ABCD is a square, diagonals AC and BD meet at O. The number of pairs of congruent triangles with vertex O are

In the given figure CE || DB then the value of x° is

The correct statement out of the following is 

If the diagonal of a rhombus are equal, then the rhombus is a

If bisectors of ∠A and ∠B of a quadrilateral ABCD meet at O, then ∠AOB is 

The interior angle made by the side in a parallelogram is 90° then the parallelogram is a

Which of the following statement is correct? 

The angles of the triangle are 3x – 40, x + 20 and 2x – 10 then the value of x is

PQ and RS are two equal chords of a circle with centre O such that ∠POQ = 70°, then ∠ORS =

A chord is at a distance of 15 cm from the centre of the circle of radius 25 cm. The length of the chord is

In the figure, O is the centre of the circle and ∠ACB = 40° then ∠AOB =

In a cyclic quadrilaterals ABCD, ∠A = 4x, ∠C = 2x the value of x is

In the figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is

In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ∠QRS = 100°, then ∠TVS =

If one angle of a cyclic quadrilateral is 75°, then the opposite angle is 

In the figure, ABCD is a cyclic quadrilateral in which DC produced to E and CF is drawn parallel to AB such that ∠ADC = 80° and ∠ECF = 20°, then BAD =?

AD is a diameter of a circle and AB is a chord If AD = 30 cm and AB = 24 cm then the distance of AB from the centre of the circle is

In the given figure, If OP = 17 cm, PQ = 30 cm and OS is perpendicular to PQ, then RS is