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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. If ΔABC ~ ΔFED, the AB/? = ?/ED.
Ans. AB/FE = BC/ED
Question. If two triangles are similar, their corresponding sides are __________.
Ans. Proportional
Question. If the sides of two similar triangles are in the ratio 4 : 9, then the areas of these triangles are in the ratio 16 : 81.
Ans. True
Question. The Basic Proportionality Theorem was given by Pythagoras.
Ans. False
Question. The ratio of areas of two similar triangles is equal to the
(a) ratio of their corresponding sides.
(b) ratio of their corresponding altitudes.
(c) ratio of the square of their corresponding sides.
(d) ratio of their perimeter.
Ans. (c) ratio of the square of their corresponding sides.
Question. The length of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is
(a) 9 cm
(b) 10 cm
(c) 8 cm
(d) 20 cm
Ans. (b) 10 cm
Question. In a right triangle ABC, in which ∠C = 90° amd CD ⊥ AB. If BC = a, CA = b, AB = c and CD = p, then
(a) 1/p2 = 1/a2 + 1/b2
(b) 1/p2 ≠ 1/a2 + 1/b2
(c) 1/p2 < 1/a2 + 1/b2
(d) 1/p2 > 1/a2 + 1/b2
Ans. (a) 1/p2 = 1/a2 + 1/b2
Question. It is given that ΔABC ~ ΔPQR with BC/QR = 1/3 , then find the value of ar(ΔPRQ) / ar(ΔACB).
Ans. 1/9
Question. In the given figure, if ΔABC ~ ΔPQR, find the value of x?
Ans. AB/PQ = BC/QR ⇒ 6/4.5 = 4/x ⇒ x = 3cm
Question. In the given figure, find the value of x which will make DE || AB ?
Ans. (x+3) / (3x+19) = x/(3x+4) (By B.P.T.)
x = 2
Question. An aeroplane leaves an airport and flies due west at a speed of 2100 km/hr. At the same time, another aeroplane leaves the same place at airport and flies due south at a speed of 2000 km/hr. How far apart will be the two planes after 1 hour?
Ans.
Question. If ΔABC and ΔDEF are similar triangles such that ∠A = 45° and ∠F = 56°, then find the value ∠C.
Ans. ∠F = ∠C = 56°
Question. In the given figure, XY || QR and PX/XQ = PY/YR = 1/2 , find XY : QR.
Ans. ΔPXY ~ ΔPQR
PX/PQ = XY/QR = 1/3
∴ XY : QR = 1 : 3
Question. In the given figure, AB || DE. Find the length of CD.
Ans. ΔABC ~ ΔEDC (AA Similarity criterion)
6/3 = 5/CD
CD = 2.5 cm
Question. Perimeter of two equilateral triangles ΔABC and ΔPQR are 144 m and 96 m, Find ar (ΔABC) : ar (ΔPQR).
Ans. ar(ΔABC)/ar(ΔPQR) = (144/96)2 = 9/4
∴ ar(ΔABC) : ar(ΔPQR) = 9 : 4
Question. In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio 1 : 2. If BE = 1.5 cm find BC.
Ans. ΔBOE ~ ΔDOA (AA Similarity criterion)
BO/DO = BE/DA
1/2 = 1.5/DA
DA = 3 cm
BC = DA = 3 cm (Opposite sides of a parallelogram)
Question. In ΔABC, AD ⊥ BC such that AD2 = BD × CD. Prove that ΔABC is right angled triangle.
Ans.
Question. In figure ΔPQR is right-angled at P.M is a point on QR such that PM is perpendicular to QR. Show that PQ2 = QM × QR.
Ans.
Question. Through the vertex D of a parallelogram ABCD, a line is drawn to intersect the sides BA and BC produced at E and F respectively. Prove that DA/AE = FB/BE = FC/CD.
Ans.
ΔEAD ~ ΔEBF
EA/EB = AD/BF
⇒ BF/BE = AD/AE = (BF - AD)/(BE - AE) = (BF - BC)/BA = CF/DC
Question. In figure BN and CM are medians of a ΔABC right angled at A. Prove that 4(BN2 + CM2) = 5 BC2
Ans.
Question. In equilateral ΔABC, AD ⊥ BC. Prove that 3BC2 = 4AD2.
Ans.
ΔADB ≅ ΔADC
BD = DC
∴ BD = (1/2)BC ..(1)
In right angled ΔADB,
AB2 = AD2 + BD2
BC2 = AD2 +(BC/2)2 [∵ AB = BC = CA and from (1)]
3BC2 = 4AD2
Question. The Perimeters of two similar triangles are 30 cm and 20 cm repsectively. If one side of the first triangle is 9 cm long. Find the length of the corresponding side of the second triangle.
Ans. ΔABC ~ ΔDEF
∴ AB/DE = BC/EF = AC/DF = k
⇒ AB = kDE, BC = kEF, AC = kDF
∴ AB + BC + AC = k (DE + EF + DF)
∴ 30/20 = 9/x ⇒ x = 6 cm
Question. In the given figure, the line segment XY is Parallel to AC of ΔABC and it divides the triangle into two parts of equal areas. Prove that AX/AB = (√2-1) / √2
Ans.
Question. Sides AB and AC and median AD of ΔABC are respectively proportional to sides PQ and PR and median PM of ΔPQR. Show that ΔABC ~ ΔPQR.
Ans. In ΔABC and ΔPQR
AB/PQ = AC/PR = AD/PM ...(1)
Extend AD to a point E s.t. AD = DE and PM to point L s.t. PM = ML
∴ quadrilateral of ABEC and PQLR are parallelogram
(∵ diagonals bisect each other)
Δ AC = BE, AB = EC
PR = QL, PQ = LR ....(2)
From (1) and (2)
AB/PQ = BE/QL = 2AD/2PM = AE/PL
∴ ΔABE ~ ΔPQL
∴ ∠ABE = ∠PQL ...(3)
Similarly, ΔAEC ~ ∠PLR
⇒ ∠CAE = ∠RPL ...(4)
⇒ ∠CAB = ∠RPQ (from 3 and 4)
∴ In ΔABC and ΔPQR
AB/PQ = AC/PR and ∠CAB = ∠RPQ
∴ ΔABC ~ ΔPQR
Question. In figure if ΔABC ~ ΔDEF and their sides of lengths (in cm) are marked along them, then find the lengths of sides of each triangle.
Ans.
Please click on below link to download CBSE Class 10 Mathematics Triangles Worksheet Set C
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A |
CBSE Class 10 Maths Probabilty Worksheet |
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Chapter 6 Triangles worksheet Mathematics CBSE Class 10
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Chapter 6 Triangles CBSE Class 10 Mathematics Worksheet
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Worksheet for CBSE Mathematics Class 10 Chapter 6 Triangles
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