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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
(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
(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.
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.
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.
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.
Ans. Draw EO || AB, DE/EA =DO/OB (In ΔADB) and DE/EA = OC/OA (In ΔACD)
(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.
Ans. Draw AX ⊥ BC and DY ⊥ BC
ar(ΔABC) / ar(ΔDBC) = ((1/2)×BC×AX) / ((1/2)×BC×DY) = AX/DY ..(1)
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.
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.
Ans.
Question. If AD and PS are medians of ΔABC and ΔPQR respectively where ΔABC ~ ΔPQR, Prove that AB/PQ = AD/PS.
Ans.
Question. In an Obtuse ΔABC (∠B is obtuse), AD is perpendicular to CB produced. Then prove that AC2 = AB2 + BC2 + 2BC × BD.
Ans.
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)
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.
Please click on below link to download CBSE Class 10 Mathematics Triangles Worksheet Set A
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A |
CBSE Class 10 Maths Probabilty Worksheet |
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.
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