# Worksheets For Class 10 Mathematics Triangles

Class 10 Triangles Worksheet have been designed as per the latest pattern for CBSE, NCERT and KVS for Grade 10. Students are always suggested to solve printable worksheets for Mathematics Triangles Grade 10 as they can be really helpful to clear their concepts and improve problem solving skills. We at worksheetsbag.com have provided here free PDF worksheets for students in standard 10 so that you can easily take print of these test sheets and use them daily for practice. All worksheets are easy to download and have been designed by teachers of Class 10 for benefit of students and is available for free download.

## Mathematics Triangles Worksheets for Class 10

We have provided chapter-wise worksheets for class 10 Mathematics Triangles which the students can download in Pdf format for free. This is the best collection of Mathematics Triangles standard 10th worksheets with important questions and answers for each grade 10th Mathematics Triangles chapter so that the students are able to properly practice and gain more marks in Class 10 Mathematics Triangles class tests and exams.

Question. Find x and if DE || BC.

(A) 1
(B) 2
(C) 3
(D) 4

B

Question. In a triangle ABC, D is the mid-point of AB, E is the mid-point of DB and F is the midpoint of BC. If the area of ΔABCis 96, then the area of ΔAEF is ………..
(A) 16
(B) 24
(C) 32
(D) 36

D

Question. Find y if DE || BC.

(A) 250
(B) 300
(C) 40
(D) 45

C

In fig., a rectangle is divided into four triangles x, y, z, w. The ratio of area x to area y is 2 : 3 and the ratio of area y to area z is 2 : 3. If area of w is 168cm2. Find the area of the rectangle.

(A) 324cm2
(B) 624cm2
(C) 430cm2
(D) None of these

D

Question. In the given figure, AB = AC and CD || BA. The value of x is

(A) 520
(B) 760
(C) 1560
(D) 1040

D

Question. If the two polygons are similar then find the value of x.

(A) 6
(B) 16/3
(C) 17/3
(D) 8

B

Question. A kite got stuck on top of a 20 feet wall. A ladder is used by person to get the kite. It should be placed in such a manner that the top of ladder should rest on top of the wall and bottom of the ladder should be 15 feet away from the bottom of wall. Height of the ladder is:
(A) 22 feet
(B) 20 feet
(C) 25 feet
(D)14 feet

C

Question. If AP and BP are the bisectors of the angle A and angle B of a parallelogram ABCD, then value of the angle APB is:

(A) 30o
(B) 45o
(C) 60o
(D) 90

D

Question. If ΔABC has ∠B = 900 and D and E are points on BC where when connected to A, AD and AE trisects the angle A. Then
(A) AE2 = 3AC2 /8 + 5AD2/8
(B) AC2 = 3AE2 /8 + 5AD2/8
(C) AC2 = AE2 = AD2
(D) none of these

A

Question. In the figure, PQ = QR = RS = SP = SQ = 6 cm and PT = RT = 14 cm. The length ST is:

(A) 4√10 cm
(B) (7 √3 – 2) cm
(C) 10 cm
(D) 11 cm

C

Question. If ΔABCis a isosceles triangle where AB = BC and DE || BC, so if AD = 1.8 cm and CE = 5. 2 cm then AC is :
(A) 5.2 cm
(B) 6 cm
(C) 8 cm
(D)7cm

D

Question. ABCD is a square of area of 4 square units which is divided into 4 non overlapping triangles as shown in figure, then sum of perimeters of the triangles so formed is

(A) 8(2 + √2)
(B) 8(1 + √2)
(C) 4(2 + √2)
(D) 4(1 + √2)

B

Question. A ship started from the base of a light house. Height of the ship is 25 ft. The ship is travelling with a speed of 10 feet/sec. So after 5 seconds what is the length if the ship’s shadow on water if height of the light house is 50 ft.
(A) 60 ft
(B) 50 ft
(C) 25 ft
(D) 100ft

B

Question. If DE || BC then

(A) AB/AC = BC/BE
(B) AB/BC = DE/BE
(D) none of these

C

Question. In the figure ∠D = 900 AB =16 cm BC =12 cm and CA = 6cm then CD is

(A) 13/6 cm
(B) 17/6 cm
(C) 19/6 cm
(D) 18/5cm

C

Question. ABCD is a quadrilateral in which zy = y/x = xw = k and k ϵ z. also {w, x} < 900 and {y, z}> 900, then the difference between the greatest angle and the smallest angle is:
(A) 1280
(B) 1680
(C) 1010
(D) 990

B

Question. In a ΔABC,DE intersects AB and AC at point D and E respectively. If AB = 9, AD = 6, AE = 4, AC = 6 then line DE and BC are
(A) same
(B) parallel
(C) perpendicular
(D) none of these

B

Question. Here BG || CD and FG || DE when which of the following are correct?

(A) AC/BG = AE/DE
(B) AB/AC = AF/AE
(D) none of these

B

Question. ABC is a triangle in which D, E and F are the mid-point of the sides of AC, BC and AB respectively . what is the ratio of the area of the shaded to the unshaded region in the triangle?

(A) 3 : 2
(B) 1 : 1
(C) 3 : 7
(D) None of these

B

Question. Here QN || LM and QO || LN, so which of the following is correct?

(A) POxPN  = NMxON
(B) POxMN = PNxON
(C) ONxNL = OQ
(D) none of these

B

Question. In the given figure, ABCD is trapezium in which AB CD and its diagonals intersect at O. If AO= (3x –1) cm, OC = (5x –3) cm, BO = (2x+1) cm andOD(6x –5) cm, find the value of x

(A) 1/2
(B) 3
(C) 4
(D) 2

D

Question. Let A by any point inside the rectangle KLMN. Then
(A) KL2 + LM = NM2 + MA
(B) KA2 + LM = KN2 + AL
(C) AK2 + AM = AL2 + AN
(D) none of these

C

Question. If DG is the bisector of the angle ∠D in the ΔDEF and DE = 6, DF = 8, EF = 10, then EG =
(A) 15/7
(B) 34/7
(C) 40/7
(D) 30/7

D

Question. There are two squares s1 and s2 with areas 8 and 9 square units, respectively s1 is inscribed within s2, with one comes of s1 on each side of s2. The corners of the smaller square divides the sides of the bigger square into two segments, one of the length a and the other of length b, where b>a. a possible value of b/a is.
(A) ≥ 14 and < 17
(B) >17
(C) ≥ 11 and < 14
(D) None of these

A

Question. If two lines DE and LM bisects each other and if DM = 8 cm then EL is:
(A) 8/3cm
(B) 4 cm
(C) 6 cm
(D) 8cm

D

Question. Here DR || HI || GF, HJ = 6 cm, JF = 9 cm, GI = 18 cm and GF = 12 cm then HI is:

(A) 9 cm
(B) 8 cm
(C) 6 cm
(D) 10 cm

D

Question. If ΔABC ≅ ΔDEF. If ∠A = 3x – 60and ∠D = x + 20 then ∠A is:
(A) 60
(B) 90
(C) 100
(D)

A

Question. Find x:

(A) 11.4
(B) 10.9
(C) 11.6
(D)12.2

B

Question. If AB || CD then ΔABE and ΔDCEwill be

(A) similar
(B) concreate
(C) equilateral
(D) cannot say

A

Solved Problems on Class 10 Triangles

Question. In Fig.4.5, if LM||CB and LN||CD, prove that AM/AB=AN/AD

Sol. Firstly, in ΔABC, we have
LM||CB                                                          (Given)
Therefore, by Basic Proportionality Theorem, we haveAM/AB=AL/AC         …(i)
Again, in ΔACD, we have
LN||CD                                                           (Given)
∴ By Basic Proportionality Theorem, we have AN/AD=AL/AC                      …(ii)
Now, from (i) and (ii), we have AM/AB=AN/AD.

Question. In Fig.4.3, DE||BC. If AD = x , DB = x – 2, AE = x + 2 and EC = x -1, find the value of x.
Sol. In DABC, we have
DE||BC,
⇒ x/x-2=x+2/x-1     ⇒   x(x-1)=(x_2)
⇒  x (x -1) = (x – 2) (x + 2)
⇒  x 2 – x = x2 – 4   ⇒  x = 4

Question. If ABC and DEF are similar triangles such that ∠A = 47° and ÐE = 63°, then the measures of ∠C = 70°. Is it true? Give reason.
Sol. Since ΔABC ~ΔDEF
∠A= ÐD = 47°, ∠B= ÐE = 63°
∠C =180° -(∠A + ∠B) = 180 – (47 + 63) = 70°
Given statement is true

Question. In Fig.4.6, DE||OQ and DF||OR, Show that EF||QR.

Sol. In ΔPOQ, we have
DE||OQ (Given)
By Basic Proportionality Theorem, we have PE/EQ=PD/DO          …(i)
Again, in DPOR, we have
DF||OR (Given)
∴ By Basic Proportionality Theorem, we have PD/DO=PF/FR           …(ii)
Now, from (i) and (ii), we have
PE/EQ=PF/FR  ⇒ EF||QR
[Applying the converse of Basic Proportionality Theorem in DPQR]

Question. A and B are respectively the points on the sides PQ and PR of a ΔPQR such that PQ =12 5 . cm, PA = 5 cm, BR= 6 cm and PB= 4 cm. Is AB||QR? Give reason.
Sol. PA/AQ =5/12.5-5 = 5/ 5 = 2/3
PB/BR= 4/6=2/3
Since PA/AQ=PB/BR=2/3
∴ AB||QR

Question. In triangle PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M =100° and ∠S = 25°. Is ΔQPR~ΔTSM? Why?
Sol. Since, ∠R =180°-(∠P + ∠Q) = 180° – (55° + 25°) = 100° = ÐM
∠Q = ∠S = 25°
ΔQPR ~ΔSTM
i.e., ΔQPR is not similar to ΔTSM.

Question. Prove that, 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 same ratio.
Using the above result, do the following:  In Fig. 4.2 DE||BC and BD = CE. Prove that DABC is an isosceles triangle.

Sol. Given: A triangle ABC in which a line parallel to side BC intersects other two sides AB and AC at D and E respectively.
Construction: Join BE and CD and then draw DM^AC and EN^ AB.
Proof: Area of ΔADE = 1/2(basexhight)

Question.. E and F are points on the sides PQ and PR respectively of a ΔPQR. For each of the following cases, state whether EF||QR.
(i) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(ii) PQ= 1.28 cm, PR= 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

Sol. (i) We have, PE = 4 cm, QE = 4.5 cm
PF = 8 cm, RF = 9 cmNow, PE/QE= 4/4.5=8/9
And PF/RF= 8/9
Thus, PE/QE=PF/RF,                               Therefore, EF||QR. [By the converse of Basic Proportionality Theorem]
(ii) We have,
PQ =1.28 cm, PR = 2.56 cm
PE = 0.18 cm, PF = 0.36 cm
Now, QE = PQ – PE =1.28 – 0.18 =1.10 cm
and FR = PR – PF = 2.56 – 0.36 = 2.20 cm
Now, PE/QE=0.18/1.10 =18/.10=9/55.
and, PF/FR= 0.36/220 =36/220=9/55.            ∴ PE/QE=PF/FR
Therefore, EF||QR [By the converse of Basic Proportionality Theorem]

Question.. In Fig.4.7, A, B and C are points on OP, OQ and OR respectively such that AB||PQ and AC||PR. Show that BC||QR.

Sol. In ΔOPQ, we have
AB||PQ                                                 (Given)
By Basic Proportionality Theorem, we have
OA/AP=OB/BQ                                                   …(i)
Now, in DOPR, we have
AC||PR                                                (Given)
By Basic Proportionality Theorem, we have
OA/AP=OC/CR                                                    …(ii)
From (i) and (ii), we have
OB/BQ=OC/CR
Therefore, BC||QR (Applying the converse of Basic Proportionality Theorem in ΔOQR)

Question. Using Basic Proportionality Theorem, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

Sol. Given: A ΔABC in which D is the mid-point of AB and DE is drawn parallel to BC, which meets AC at E.
To prove: AE = EC
Proof: In ΔABC, DE||BC
∴ By Basic Proportionality Theorem, we have
Now, since D is the mid-point of AB
From (i) and (ii), we have
BD/BD = AE/EC       ⇒      1 = AE/EC
⇒   AE = EC
Hence, E is the mid-point of AC.

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

Sol. Given: DABC in which D and E are the mid-points of sides AB and AC respectively.
To prove: DE||BC
Proof: Since, D and E are the mid-points of AB and AC respectively
Therefore, DE||BC (By the converse of Basic Proportionality Theorem)

## Mathematics Triangles Worksheets for Class 10 as per CBSE NCERT pattern

Parents and students are welcome to download as many worksheets as they want as we have provided all free. As you can see we have covered all topics which are there in your Class 10 Mathematics Triangles book designed as per CBSE, NCERT and KVS syllabus and examination pattern. These test papers have been used in various schools and have helped students to practice and improve their grades in school and have also helped them to appear in other school level exams. You can take printout of these chapter wise test sheets having questions relating to each topic and practice them daily so that you can thoroughly understand each concept and get better marks. As Mathematics Triangles for Class 10 is a very scoring subject, if you download and do these questions and answers on daily basis, this will help you to become master in this subject.

Benefits of Free Class 10 Triangles Worksheet

1. You can improve understanding of your concepts if you solve NCERT Class 10 Mathematics Triangles Worksheet,
2. These CBSE Class 10 Mathematics Triangles worksheets can help you to understand the pattern of questions expected in Mathematics Triangles exams.
3. All worksheets for Mathematics Triangles Class 10 for NCERT have been organized in a manner to allow easy download in PDF format
4. Parents will be easily able to understand the worksheets and give them to kids to solve
5. Will help you to quickly revise all chapters of Class 10 Mathematics Triangles textbook
6. CBSE Class 10 Mathematics Triangles Workbook will surely help to improve knowledge of this subject

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