#### Chapters

## Chapter 5: Geometry

### Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 5 Geometry Exercise 5.1 [Pages 165 - 166]

#### Fill in the blanks with the correct term mention in option.

Corresponding sides of similar triangles are _________

in proportion

similar

corresponding

congruent

shape

area

equal

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

in proportion

similar

corresponding

congruent

shape

area

equal

In any triangle _______ sides are opposite to equal angles

in proportion

similar

corresponding

congruent

shape

area

equal

The symbol ≡ is used to represent ________ triangles

in proportion

similar

corresponding

congruent

shape

area

equal

The symbol ~ is used to represent _________ triangles

in proportion

similar

corresponding

congruent

shape

area

equal

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.

#### Objective Type Questions

Two similar triangles will always have ________ angles

acute

obtuse

right

matching

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

∠Q = ∠Y

∠P = ∠Y

∠Q = ∠X

∠P = ∠Z

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

90 m

91 m

92 m

93 m

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

50°

60°

70°

80°

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

AB = BD

BD < CD

AC = CD

BC = CD

### Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 5 Geometry Exercise 5.2 [Pages 177 - 179]

#### Fill in the blanks:

If in a ΔPQR, PR^{2} = PQ^{2} + QR^{2}, 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, l^{2} = ________

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 _______

#### Say True or False

8, 15, 17 is a Pythagorean triplet

True

False

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

True

False

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

True

False

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

True

False

The incentre is equidistant from all the vertices of a triangle

True

False

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

#### Objective Type Questions

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

30°

40°

45°

55°

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

28 cm

20 cm

24 cm

21 cm

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

609 cm

^{2}580 cm

^{2}420 cm

^{2}210 cm

^{2}

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

25, 36, 59

10, 24, 26

36, 39, 45

20, 48, 52

### Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 5 Geometry Exercise 5.3 [Pages 179 - 180]

#### Miscellaneous Practice Problems

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

#### Challenging problems

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 DG^{2} = 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 = ?

### Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 5 Geometry Exercise 5.4 [Page 192]

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

### Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board Chapter 5 Geometry Exercise 5.5 [Page 209]

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

## Chapter 5: Geometry

## Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board chapter 5 - Geometry

Samacheer Kalvi solutions for Mathematics Class 8th Tamil Nadu State Board chapter 5 (Geometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Mathematics Class 8th Tamil Nadu State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Class 8th Tamil Nadu State Board chapter 5 Geometry are Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given, Construct a Quadrilateral When Its Four Sides and One Angle Are Given., Congruency of Shapes, Similar Figures, Congruence of Triangles, Criteria for Congruence of Triangles, SSS Congruence Criterion, SAS Congruence Criterion, ASA Congruence Criterion, RHS Congruence Criterion, Similarity of Triangles, The Property of the Angle Bisectors of a Triangle, Converse of Pythagoras Theorem, Point of Concurrency, Median of a Triangle, Altitudes of a Triangle, Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given, Perpendicular Bisectors of a Triangle, Construction of a Rhombus When One Side and One Angle Are Given., Construction of a Rhombus When Two Diagonals Are Given., Circumcentre of a Triangle, Right-angled Triangles and Pythagoras Property, Constructing a Trapezium When Its Two Sides and Two Angles Are Given., Constructing a Trapezium When Its Four Sides Are Given., Constructing a Parallelogram When Its Two Adjacent Sides and One Angle Are Given., Constructing a Parallelogram When Its Two Adjacent Sides and One Diagonal Are Given., Constructing a Parallelogram When Its Two Diagonals and One Included Angle Are Given., Constructing a Parallelogram When Its One Side, One Diagonal and One Angle Are Given., Construction of a Rhombus When One Side and One Diagonal Are Given., Construction of a Rhombus When One Diagonal and One Angle Are Given., Construction of a Rectangle When Its Length and Breadth Are Given., Construction of a Rectangle When a Side and a Diagonal Are Given., Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given, Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known, Constructing a trapezium when its three sides and one diagonal are given, Constructing a Trapezium When Its Three Sides and One Angle Are Given, Construction of a Square When Its Side is Given., Construction of a Square When Its Diagonal is Given..

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