CBSE Class 10 Mathematics Triangles Worksheet Set A

Read and download free pdf of CBSE Class 10 Mathematics Triangles Worksheet Set A. Download printable Mathematics Class 10 Worksheets in pdf format, CBSE Class 10 Mathematics Chapter 6 Triangles Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 10 Assignments and practice them daily to get better marks in tests and exams for Class 10. Free chapter wise worksheets with answers have been designed by Class 10 teachers as per latest examination pattern

Chapter 6 Triangles Mathematics Worksheet for Class 10

Class 10 Mathematics students should refer to the following printable worksheet in Pdf in Class 10. This test paper with questions and solutions for Class 10 Mathematics will be very useful for tests and exams and help you to score better marks

Class 10 Mathematics Chapter 6 Triangles Worksheet Pdf

 

Question. Circles with equal radii are _________ .
Ans. Congruent

Question. In ΔABC, AB = 6√3, AC = 12 cm and BC = 6 cm, then ∠B = _______ .
Ans. 90°

Question. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the _________ ratio.
Ans. Same

Question. The mid-point theorem can be proved by Basic Proprotionality Theorem.
Ans. True

Question. All the similar figures are always congruent.
Ans. False

Question. If the three sides of a triangle are a, √3a and √2a , then the measure of hte angle opposite to longest side is
(a) 45°
(b) 30°
(c) 60°
(d) 90°
Ans. (d) 90°

Question. In the following figure, QA ⊥ AB and PB ⊥ AB, then AQ is

CBSE Class 10 Mathematics Triangles_2

(a) 15 units
(b) 8 units
(c) 5 units
(d) 9 units
Ans. (a) 15 units

Question. The areas of two similar triangles are 144 cm2 and 81 cm2. If one median of the first triangle is 16 cm, length of corresponding median of the second triangle is
(a) 9 cm
(b) 27 cm
(c) 12 cm
(d) 16 cm
Ans. (c) 12 cm

Question. In the following figure, XY || QR and PX/XQ = PY/YR = 1/2, then

CBSE Class 10 Mathematics Triangles_1

(a) XY = QR
(b) XY = (1/3)QR
(c) XY2 = QR2
(d) XY = (1/2) QR
Ans. (b) XY = (1/3)QR

Question. If ΔABC ~ ΔDEF, BC = 3EF and ar (ΔABC) = 117cm2 find area (ΔDEF).
Ans. ar(ABC)/ar(DEF) = (BC/EF)2 = (3EF/EF)2 = (3/1)2
117 / ar(DEF) = 9 ⇒ ar(DEF) = 13 cm2

Question. Is the triangle with sides 12 cm, 16 cm and 18 cm a right triangle?
Ans. No, because (12)2 + (16)2 = (18)2

Question. In the given Fig., ∠M = ∠N = 46°, Express x in terms of a, b and c.

CBSE Class 10 Mathematics Triangles_3

Ans. ΔKPN ~ ΔKLM
x/a = c/(b+c)
x = ac/(b+c)

Question. If the ratio of the corresponding sides of two similar triangles is 2 : 3, then find the ratio of their corresponding attitudes.
Ans. 2 : 3

Question. Write the statement of pythagoras theorem.
Ans. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Question. In the given Fig., D and E are points on sides AB and CA of ΔABC such that ΔB = ∠AED. Show that ΔABC ~ ΔAED.

CBSE Class 10 Mathematics Triangles_4

Ans. ∠B = ∠AED (Given)
∠A = ∠A (Common)
∴ ΔABC ~ ΔAED [AA similarity criterion]

Question. In the given Fig. PQ = 24 cm, QR = 26 cm, ∠PAR = 90°, PA = 6 cm and AR = 8 cm, find ∠QPR.

CBSE Class 10 Mathematics Triangles_5

Ans. PR = √((6)2+(8)2) = 10 cm.
As QR2 = PQ2 + PR2 , therefore ∠QPR = 90°.
(By Converse of Pythagoras theorem)

Question. In the given fig., AB || DC and diagonals AC and BD intersects at O. If OA = 3x – 1 and OB = 2x + 1, OC = 5x – 3 and OD = 6x – 5, find the value of x.

CBSE Class 10 Mathematics Triangles_6

Ans. Draw EO || AB, DE/EA =DO/OB (In ΔADB) and DE/EA = OC/OA (In ΔACD)

CBSE Class 10 Mathematics Triangles_7

(3x-1)/(5x-3) = (2x+1)/(6x-5) ⇒ x = 1/2 or 2
But x = 1/2 is neglected because (5x – 3) get negative value.
So, x = 2 is the required value.

Question. In the adjoining figure ΔABC and ΔDBC are on the same base BC. AD and BC intersect at O. Prove that
area(ΔABC) / area(ΔDBC) = AO/DO.

CBSE Class 10 Mathematics Triangles_8

Ans. Draw AX ⊥ BC and DY ⊥ BC
ar(ΔABC) / ar(ΔDBC) = ((1/2)×BC×AX) / ((1/2)×BC×DY) = AX/DY    ..(1)

CBSE Class 10 Mathematics Triangles_9

ΔAXO ~ ΔDYO         [AA similarity criterion]
AX/DY = AO/DO      ...(2) (C.P.S.T.)
From (1) and (2), we get
ar(ΔABC)/ar(ΔDBC) = AO/DO

Question. Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is larger than the other by 5 cm, find the length of the other two sides.
Ans. Let sides of right angled triangle other than hypotenuse be x cm and (x + 5) cm.
By Pythagoras theorem,
(x)2 + (x + 5)2 = (25)2
x = 15 or – 20
But side is always positive, So, x = 15.
∴ Length of two sides is 15 cm and 20 cm.

Question. In ΔABC, ∠ACB = 90° and CD ⊥ AB. Prove that BC2/AC2 = BD/AD.
Ans. 

CBSE Class 10 Mathematics Triangles_10

ΔABC ~ ΔCBD
∴ BC2 = AB.BD             ...(1)
ΔABC ~ ΔACD
∴ AC2 = AB.AD             ...(2)
Divide (1) by (2), we get
BC2/AC2 = BD/AD

Question. In the figure, a point O inside ΔABC is joined to its vertices. From a point D on AO, DE is drawn parallel to AB and from a point E on BO, EF is drawn parallel to BC. Prove that DF || AC.

CBSE Class 10 Mathematics Triangles_11

Ans.

CBSE Class 10 Mathematics Triangles_12

Question. If AD and PS are medians of ΔABC and ΔPQR respectively where ΔABC ~ ΔPQR, Prove that AB/PQ = AD/PS.
Ans. 

CBSE Class 10 Mathematics Triangles_13

Question. In an Obtuse ΔABC (∠B is obtuse), AD is perpendicular to CB produced. Then prove that AC2 = AB2 + BC2 + 2BC × BD.
Ans. 

CBSE Class 10 Mathematics Triangles_14

In ΔADB
AB2 = AD2 + DB2      ...(i)
In ΔADC
AC2 = AD2 + DC2
= AD2 + (DB + BC)2
= AD2 + DB2 + BC2 + 2BC.BD
= AB2 + BC2 + 2BC.BD (Using (i))

Question. In the given figure, DE || AC. Which of the following is correct?
x = (a+b)/ay or x = ay/(a+b)

CBSE Class 10 Mathematics Triangles_15

Ans. ΔBED ~ ΔBCA
x/y = a/(a+b)
⇒ x = ay/(a+b)

Question. In an equilateral ΔABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9A D2 = 7AB2.
Ans. CBSE Class 10 Mathematics Triangles_16

 

 

CBSE Class 10 Mathematics Triangles Worksheet Set A 1

CBSE Class 10 Mathematics Triangles Worksheet Set A 2

CBSE Class 10 Mathematics Triangles Worksheet Set A 3

 

Please click on below link to download CBSE Class 10 Mathematics Triangles Worksheet Set A

Chapter 6 Triangles CBSE Class 10 Mathematics Worksheet

The above practice worksheet for Chapter 6 Triangles has been designed as per the current syllabus for Class 10 Mathematics released by CBSE. Students studying in Class 10 can easily download in Pdf format and practice the questions and answers given in the above practice worksheet for Class 10 Mathematics on a daily basis. All the latest practice worksheets with solutions have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better scores in their examinations. Studiestoday is the best portal for Printable Worksheets for Class 10 Mathematics students to get all the latest study material free of cost. Teachers of studiestoday have referred to the NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 worksheet. After solving the questions given in the practice sheet which have been developed as per the latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter. We have also provided a lot of other Worksheets for Class 10 Mathematics which you can use to further make yourself better in Mathematics.

Where can I download latest CBSE Practice worksheets for Class 10 Mathematics Chapter 6 Triangles

You can download the CBSE Practice worksheets for Class 10 Mathematics Chapter 6 Triangles for the latest session from StudiesToday.com

Are the Class 10 Mathematics Chapter 6 Triangles Practice worksheets available for the latest session

Yes, the Practice worksheets issued for Chapter 6 Triangles Class 10 Mathematics have been made available here for the latest academic session

Is there any charge for the Practice worksheets for Class 10 Mathematics Chapter 6 Triangles

There is no charge for the Practice worksheets for Class 10 CBSE Mathematics Chapter 6 Triangles you can download everything free

How can I improve my scores by solving questions given in Practice worksheets in Chapter 6 Triangles Class 10 Mathematics

Regular revision of practice worksheets given on studiestoday for Class 10 subject Mathematics Chapter 6 Triangles can help you to score better marks in exams

Are there any websites that offer free Practice test papers for Class 10 Mathematics Chapter 6 Triangles

Yes, studiestoday.com provides all the latest Class 10 Mathematics Chapter 6 Triangles test practice sheets with answers based on the latest books for the current academic session