CBSE Class 10 Mathematics Triangles Worksheet Set H

Read and download free pdf of CBSE Class 10 Mathematics Triangles Worksheet Set H. Students and teachers of Class 10 Mathematics can get free printable Worksheets for Class 10 Mathematics Chapter 6 Triangles in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 10 students should practice questions and answers given here for Mathematics in Class 10 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 10 Mathematics Worksheets prepared by teachers as per the latest Mathematics books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

Worksheet for Class 10 Mathematics Chapter 6 Triangles

Class 10 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 6 Triangles in Class 10. This test paper with questions and answers for Class 10 will be very useful for exams and help you to score good marks

Class 10 Mathematics Worksheet for Chapter 6 Triangles

 

Triangles

Q.- Prove that the area of the triangle BCE described on one side BC of a square ABCD as base is one half the area of the similar triangle ACF described on the diagonal AC as base.
 
Sol. ABCD is a square. ΔBCE is described on side BC is similar to ΔACF described on diagonal AC.
Since ABCD is a square. Therefore,
triangles notes 67
Q.- D, E, F are the mid-point of the sides BC, CA and AB respectively of a ΔABC. Determine the ratio of the areas of ΔDEF and ΔABC.
 
Sol. Since D and E are the mid-points of the sides BC and AB respectively of Δ ABC. Therefore,
DE || BA
Δ DE || FA ....(i)

triangles notes 68

Since D and F are mid-points of the sides BC and AB respectively of ΔABC. Therefore,
DF || CA => DF || AE
From (i), and (ii), we conclude that AFDE is a parallelogram.
Similarly, BDEF is a parallelogram.
 
Now, in ΔDEF and ΔABC, we have
∠FDE = ∠A
[Opposite angles of parallelogram AFDE] and, ∠DEF = ∠B
[Opposite angles of parallelogram BDEF]
So, by AA-similarity criterion, we have
ΔDEF ~ ΔABC

triangles notes 69

Hence, Area (ΔDEF) : Area (ΔABC) = 1 : 4.
 
Q.- D and E are points on the sides AB and AC respectively of a ΔABC such that DE || BC and divides ΔABC into two parts, equal in area. Find BD/AB.
 
Sol. We have,
Area (ΔADE) = Area (trapezium BCED)
=> Area (ΔADE) + Area (ΔADE)
= Area (trapezium BCED) + Area (ΔADE)
=>  2 Area (ΔADE) = Area (ΔABC)
In ΔADE and ΔABC, we have
∠ADE = ∠B
[DE || BC  ∠ADE = ∠B (Corresponding angles)]
and, ∠A = ∠A [Common]
∴ ΔADE ~ ΔABC

triangles notes 70

triangles notes 71

Q.- Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25.Find the ratio of their corresponding heights.
 
Sol. Let ΔABC and ΔDEF be the given triangles
such that AB = AC and DE = DF, ∠A = ∠D.

triangles notes 72

triangles notes 73

Q.- In the given figure, DE || BC and DE : BC = 3 : 5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.

triangles notes 74

Key Points

Similar Figures: Two figures having similar shapes (size may or may not same), called Similar figures.

Examples: (a) & (b) & (c) &

A pair of Circles A pair of squares A pair of Equ. Triangles

- Pairs of all regular polygons, containing equal number of sides are examples of Similar Figures.

- Similar Triangles: Two Triangles are said to be similar if

(a) Their corresponding angles are equal ( also called Equiangular Triangles)

(b) Ratio of their corresponding sides are equal/proportional

- All congruent figures are similar but similar figures may /may not congruent

- Conditions for similarity of two Triangles

(a) AAA criterion/A-A corollary

(b) SAS similarity criterion

(c) SSS similarity criterion (where ‘S’ stands for ratio of corresponding sides of two Triangles)

Important Theorems of the topicTriangles

(a) Basic Proportionality Theorem (B.P.T.)/Thale’s Theorem

(b) Converse of B.P.T.

(c) Area related theorem of Similar Triangles

(d) Pythagoras Theorem

(e) Converse of Pythagoras Theorem

Level I

(1) In the figure XY ∕∕ QR , PQ/ XQ = 7/3 and PR =6.3cm then find YR

(2) If ΔABC ~ Δ DEF and their areas be 64cm2& 121cm2 respectively , then find BC if EF =15.4 cm

(3) ABC is an isosceles Δ ,right angled at C then prove that AB2 = 2AC2

(4) If ΔABC ~ Δ DEF, ∟A=460, ∟E= 620 then the measure of ∟C=720. Is it true? Give reason.

(5) The ratio of the corresponding sides of two similar triangles is 16:25 then find the ratio of their perimeters.

(6) A man goes 24 km in due east and then He goes 10 km in due north. How far is He from the starting Point?

(7) The length of the diagonals of a rhombus is 16cm & 12cm respectively then find the perimeter of the rhombus.

(8) In the figure LM ∕∕CB and LN ∕∕ CD then prove that AM/AB = AN /AD

(9) Which one is the sides of a right angled triangles among the following (a) 6cm,8cm & 11cm (b) 3cm,4cm & 6cm (c) 5cm , 12cm & 13cm

Level II

(1) In the figure ABD is a triangle right angled at A and AC is perpendicular to BD then show that AC2= BC x DC

(2) Two poles of height 10m & 15 m stand vertically on a plane ground. If the distance between their feet is 5√3m then find the distance between their tops.

(3) D & E are the points on the sides AB & AC of ΔABC, as shown in the figure. If ∟B = ∟AED then show that ΔABC ~ΔAED

(4) In the adjoining figure AB ∕∕ DC and diagonal AC & BD intersect at point O. If AO = (3x-1)cm , OB= (2x+1)cm, OC=(5x-3 )cm and OD=( 6x-5)cm then find the value of x.

(5) In the figure D &E trisect BC. Prove that 8AE2= 3AC2+ 5AD2

(6) In the figure OA/OC = OD /OB then prove that ∟A= ∟C

Please click the link below to download CBSE Class 10 Mathematics Worksheet - Triangles (6)

Worksheet for CBSE Mathematics Class 10 Chapter 6 Triangles

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