Construct a triangle with sides 5 cm , 6 cm and 7 cm and then another triangle whose sides are 7 5 of the corresponding sides of the first triangle.

Steps of Construction : Step 1: Draw a line segment, A B = 5 cm . Step 2: With A as centre, draw an arc of radius 6 cm . Step 3: With B as centre and radius equal to 7 cm , cut an arc on the previous arc and name it C . Step 4: Join B C and A C . Thus, Δ A B C is obtained. Step 5: Draw a ray A R on the side which is opposite to the point C . Mark points A 1 , A 2 , . . . . A 7 which are equidistant to each other on the same ray. Step 6: Join A 5 B and draw its parallel from A 7 to extension of A B , mark B ' as shown. From B ' draw a parallel to B C to extension of B C and mark C ' . Thus. the triangle A B ' C ' is the required triangle, each of whose sides is 7 5 the corresponding sides of △ A B C .

E M B I B E

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 53

EASY

10th Tamil Nadu Board

IMPORTANT

Earn 100

Prove that the external angle bisectors of a triangle intersect their opposite sides at three collinear points.

Important Questions on Geometry

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 54

Construct a triangle with sides

5 cm, 6 cm

and

7 cm

and then another triangle whose sides are

\frac{7}{5}

of the corresponding sides of the first triangle.

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 55

In triangle $△ P Q R$ , $E$ and $F$ are points on the sides $P Q$ and $P R$ respectively. Given $PQ = 1.28 cm, PR = 2.56 cm, PE = 1.8 cm$ and $PF = 3.6 cm$ . State whether $E F ∥ Q R$ or not?

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 56

Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 57

Prove that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side. (Using basic proportionality theorem)

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 58

Two triangles

QPR

and

QSR,

right-angled at

P

and

S

respectively are drawn on the same base

QR

and on the same side of

QR

. If

PR

and

SQ

intersect at

T

, prove that

PT \times TR = ST \times TQ

.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 59

In the figure,

A, B

and

C

are points on

O P, O Q

and

O R

respectively such that

A B ∥ P Q

and

A C ∥ P R

. Show that

B C ∥ Q R

.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 60

Using the converse of Basic Proportionality Theorem (BPT), prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Geometry>Exercise>Q 61

If the points