Samacheer Kalvi solutions for Mathematics [English] Class 8 TN Board chapter 5 - Geometry [Latest edition]

Corresponding sides of similar triangles are _________

Similar triangles have the same ________ but not necessarily the same size

In any triangle _______ sides are opposite to equal angles

The symbol ≡ is used to represent ________ triangles

The symbol ~ is used to represent _________ triangles

In the given figure, ∠CIP ≡ ∠COP and ∠HIP ≡ ∠HOP. Prove that IP ≡ OP.

In the given figure, AC ≡ AD and ∠CBD ≡ ∠DEC. Prove that ∆BCF ≡ ∆EDF.

In the given figure, ΔBCD is isosceles with base BD and ∠BAE ≡∠DEA. Prove that AB ≡ ED

In the given figure, D is the midpoint of OE and ∠CDE = 90°. Prove that ΔODC ≡ ΔEDC

Is ΔPRQ ≡ ΔQSP? Why?

From the given figure, prove that ΔABC ~ ΔEDF

In the given figure YH || TE. Prove that ΔWHY ~ ΔWET and also find HE and TE

In the given figure, if ΔEAT ~ ΔBUN, find the measure of all angles.

In the given figure, UB || AT and CU ≡ CB Prove that ΔCUB ~ ΔCAT and hence ΔCAT is isosceles.

Two similar triangles will always have ________ angles

If in triangles PQR and XYZ, `"PQ"/"XY" = "QR"/"ZX"` then they will be similar if

A flag pole 15 m high casts a shadow of 3 m at 10 a.m. The shadow cast by a building at the same time is 18.6 m. The height of the building is

If ∆ABC – ∆PQR in which ∠A = 53° and ∠Q = 77°, then ∠R is

In the figure, which of the following statements is true?

If in a ΔPQR, PR² = PQ² + QR², then the right angle of ∆PQR is at the vertex ________

If ‘l‘ and ‘m’ are the legs and ‘n’ is the hypotenuse of a right angled triangle then, l² = ________

If the sides of a triangle are in the ratio 5 : 12 : 13 then, it is ________

The medians of a triangle cross each other at _______ 

The centroid of a triangle divides each medians in the ratio _______

8, 15, 17 is a Pythagorean triplet

In a right angled triangle, the hypotenuse is the greatest side

In any triangle the centroid and the incentre are located inside the triangle

The centroid, orthocentre, and incentre of a triangle are collinear

The incentre is equidistant from all the vertices of a triangle

Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem

8, 15, 17

Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem

12, 13, 15

Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem

30, 40, 50

Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem

9, 40, 41

Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem

24, 45, 51

Find the unknown side in the following triangles

Find the unknown side in the following triangles

Find the unknown side in the following triangles

An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height

Find the distance between the helicopter and the ship

In triangle ABC, line I, is a perpendicular bisector of BC.
If BC = 12 cm, SM = 8 cm, find CS

Identify the centroid of ∆PQR

Name the orthocentre of ∆PQR

In the given figure, A is the midpoint of YZ and G is the centroid of the triangle XYZ. If the length of GA is 3 cm, find XA

If I is the incentre of ∆XYZ, ∠IYZ = 30° and ∠IZY = 40°, find ∠YXZ

If ∆GUT is isosceles and right angled, then ∠TUG is ________

The hypotenuse of a right angled triangle of sides 12 cm and 16 cm is __________

The area of a rectangle of length 21 cm and diagonal 29 cm is __________

The sides of a right angled triangle are in the ratio 5 : 12 : 13 and its perimeter is 120 units then, the sides are ______________

In the figure, given that ∠1 = ∠2 and ∠3 ≡ ∠4. Prove that ∆MUG ≡ ∆TUB

From the figure, prove that ∆SUN ~ ∆RAY

The height of a tower is measured by a mirror on the ground at R by which the top of the tower’s reflection is seen. Find the height of the tower. If ∆PQR ~ ∆STR

Find the length of the support cable required to support the tower with the floor

Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Give reason

In the figure, ∠TMA ≡∠IAM and ∠TAM ≡ ∠IMA. P is the midpoint of MI and N is the midpoint of AI. Prove that ΔPIN ~ ΔATM

In the figure, if ∠FEG ≡ ∠1 then, prove that DG² = DE.DF

The diagonals of the rhombus is 12 cm and 16 cm. Find its perimeter. (Hint: the diagonals of rhombus bisect each other at right angles)

In the figure, find AR

In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following

If DE = 44, then DM = ?

In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following

If PD = 12, then PN = ?

In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following

If DO = 8, then FD = ?

In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following

If OE = 36 then EP = ?

Construct the following quadrilaterals with the given measurements and also find their area.

ABCD, AB = 5 cm, BC = 4.5 cm, CD = 3.8 cm, DA = 4.4 cm and AC = 6.2 cm

Construct the following quadrilaterals with the given measurements and also find their area.

PLAY, PL = 7 cm, LA = 6 cm, AY = 6 cm, PA = 8 cm and LY = 7 cm

Construct the following quadrilaterals with the given measurements and also find their area.

PQRS, PQ = QR = 3.5 cm, RS = 5.2 cm, SP = 5.3 cm and ∠Q = 120°

Construct the following quadrilaterals with the given measurements and also find their area.

MIND, MI = 3.6 cm, ND = 4 cm, MD = 4 cm, ∠M = 50° and ∠D = 100°

Construct the following quadrilaterals with the given measurements and also find their area.

AGRI, AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°

Construct the following trapeziums with the given measures and also find their area.

AIMS with `bar("AI") || bar("SM")`, = 6 cm, IM = 5 cm, AM = 9 cm and MS = 6.5 cm

Construct the following trapeziums with the given measures and also find their area.

CUTE with `bar("CU") || bar("ET")`, CU = 7 cm, ∠UCE = 80° CE = 6 cm and TE = 5 cm

Construct the following trapeziums with the given measures and also find their area.

ARMY with `bar("AR") || bar("YM")`, AR = 7 cm, RM = 6.5 cm ∠RAY = 100° and ∠ARM = 60°

Construct the following trapeziums with the given measures and also find their area.

CITY with `bar("CI") || bar("YT")`, CI = 7 cm, IT = 5.5 cm, TY = 4 cm and YC = 6 cm

Construct the following parallelograms with the given measurements and find their area.

ARTS, AR = 6 cm, RT = 5 cm and ∠ART = 70°

Construct the following parallelograms with the given measurements and find their area.

CAMP, CA = 6 cm, AP = 8 cm and CP = 5.5 cm

Construct the following parallelograms with the given measurements and find their area.

EARN, ER = 10 cm, AN = 7 cm and ∠EOA = 110° where `bar("ER")` and `bar("AN")` intersect at O

Construct the following parallelograms with the given measurements and find their area.

GAIN, GA = 7.5 cm, GI = 9 cm and ∠GAI = 100°

Construct the following rhombuses with the given measurements and also find their area.

FACE, FA = 6 cm and FC = 8 cm

Construct the following rhombuses with the given measurements and also find their area.

CAKE, CA = 5 cm and ∠A = 65°

Construct the following rhombuses with the given measurements and also find their area.

LUCK, LC = 7.8 cm and UK = 6 cm

Construct the following rhombuses with the given measurements and also find their area.

PARK, PR = 9 cm and ∠P = 70°

Construct the following rectangles with the given measurements and also find their area.

HAND, HA = 7 cm and AN = 4 cm

Construct the following rectangles with the given measurements and also find their area.

LAND, LA = 8 cm and AD = 10 cm

Construct the following squares with the given measurements and also find their area.

EAST, EA = 6.5 cm

Construct the following squares with the given measurements and also find their area.

WEST, WS = 7.5 cm