CBSE Class 10 Mathematics Triangles MCQs Set D

Question. In the Fig., ΔODC ~ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠OAB.

(a) 55°
(b) 70°
(c) 125°
(d) 110°

Answer: A

Question. DE is drawn parallel to the base BC of a ΔABC, meeting AB at D and AC at E. If AB = 4 and CE = 2cm, find AE.
(a) 8cm
(b) 6cm
(c) 4cm
(d) 2cm

Answer: B

Question. In the given figure, P and Q are points on the sides AB and AC respectively of a ΔABC. PQ‖BC and divides the ΔABC into 2 parts, equal in area. The ratio of PA:PB =

(a) 1:1
(b) (√2 – 1):√2
(c) 1:√2
(d) 1: (√2 – 1)

Answer: D

Question. In the given fig. DE || BC, ∠ADE = 70° and ∠BAC = 50°, then angle ∠BCA =

(a) 50°
(b) 60°
(c) 70°
(d) 80°

Answer: B

Question. In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE parallel to BC?

(a) Yes
(b) No
(c) Neither Yes nor No
(d) None of these

Answer: B

Question. In the given figure, DE‖BC. The value of EC is

(a) 1.5cm
(b) 3cm
(c) 2cm
(d) 1cm

Answer: C

Question. It is given that ΔABC~ ΔDEF with BC/EF = 1/3. Then ar(Δ𝐷DF)/ar(ΔBCA) is equal to
(a) 9
(b) 3
(c) 1/3
(d) 1/9

Answer: A

Question. The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, then the length of QR is
(a) 4cm
(b) 4.5cm
(c) 3cm
(d) 6cm

Answer: D

Question. The areas of two similar triangles ABC and DEF are 36 cm2and 81 cm2 respectively. If EF = 6.75 cm, find BC.
(a) 6cm
(b) 9cm
(c) 5.5cm
(d) 4.5cm

Answer: D

Question. In the given figure, express x in terms of a, b and c

(a) 𝑥 = ab/𝑎+𝑏
(b) 𝑥 = ab/b+c
(c) 𝑥 = bc/b+c
(d) 𝑥 = ac/a+b

Answer: B

Question. In the Fig., if LM || CB and LN || CD, then

(a) AM/AB = AN/AD
(b) AM/AB = AN/ND
(c) AL/AC = AN/ND
(d) None of these.

Answer: A

Question. ΔABC is an equilateral triangle with each side of length 2p. If AD⊥BC. Then the value of AD is

(a) √3
(b) √3p
(c) 2p
(d) 4p

Answer: B

Question. If ΔABC ~ ΔAPQ and ar(ΔAPQ) = 4[ar(ΔABC)], then the ratio of BC to PQ is
(a) 2:1
(b) 1:2
(c) 1:4
(d) 4:1

Answer: B

Question. The length of the side of a square whose diagonal is 16cm, is
(a) 8√2cm
(b) 2√8cm
(c) 4√2 cm
(d) 2√2 cm.

Answer: A

Question. Two poles of height 6m and 11m stand vertically upright on a plane ground. If the distance between their foot is 12m, then distance between their tops is
(a) 12m
(b) 14m
(c) 13m
(d) 11m

Answer: C

Question. The areas of two similar triangles are 81cm2 and 49cm2 respectively, then the ratio of their corresponding medians is
(a) 7:9
(b) 9:8/1
(c) 9:7
(d) 81:7

Answer: C

Question. Sides of two similar triangles are in the ratio 4:9. Ares of these triangles are in the ratio
(a) 2:3
(b) 4:9
(c) 81:16
(d) 16:81

Answer: D

Question. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
(a) 56m
(b) 24m
(c) 21m
(d) 42m

Answer: D

Question. O is the point of intersection of two equal chords AB and CD such that OB = OD, then triangles OAC and ODB are

(a) Equilateral but not similar
(b) Isosceles but not similar
(c) Equilateral and similar
(d) Isosceles and similar

Answer: D

Question. A 5m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6m towards the wall, then the distance by which the top of the ladder would slide upwards on the wall is
(a) 0.6m
(b) 0.2m
(c) 0.4m
(d) 0.8m

Answer: D

Question. The lengths of the diagonals of a rhombus are 30cm and 40cm. The length of the side of the rhombus is
(a) 20cm
(b) 25cm
(c) 10cm
(d) 15cm

Answer: B

Question. The perimeter of two similar triangles ABC and LMN are 60cm and 48cm respectively. If LM = 8cm then the length of AB is
(a) 20cm
(b) 15cm
(c) 10cm
(d) 25cm

Answer: C

Question. In an equilateral triangle PQR if PS ┴ QR then PS2 = ______
(a) 5RS2
(b) 4RS2
(c) RS2
(d) 3RS2

Answer: D

Question. The length of the hypotenuse of an isosceles right triangle whose one side is 3√2 is
(a) 6cm
(b) 9cm
(c) 18cm
(d) 27cm

Answer: A

Question. A chord of a circle radius 5 cm subtends a right angle at the centre. The length of the chord is
(a) 10cm
(b) 5√2cm
(c) 15√2 cm
(d) 20cm

Answer: B

(CASE STUDY BASED QUESTIONS)

1. Observe the below given figures carefully and answer the questions

Question. Which among the above shown figures are congruent figures?
a) A and C
b) E and F
c) D and F
d) B and F

Answer: D

Question. Tick the correct statement-
a) All similar figures are congruent.
b) All congruent figures are similar.
c) The criterion for similarity and congruency is same.
d) Similar figures have same size and shape.

Answer: B

Question. If a line divides any two sides of the triangle in the same ratio, then the line is parallel to the third side. The statement depicts which theorem-
a) Pythagoras
b) Thales Theorem
c) Converse of Thales theorem
d) Converse of Pythagoras theorem.

Answer: C

Question. Using the concept of similarity, the height of the building is

a) 20ft
b) 15ft
c) 10ft
d) 7 ft

Answer: C

Question. The height of the tree, when its shadow is 102 ft long and at the same time a man 6ft high standing in the same straight line casts a shadow 17ft is

a) 14ft
b) 24ft
c) 36ft
d) 12ft

Answer: C

2. Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few questions came to his mind while making the kite. Give answers to his questions by looking at the figure.

Question. Rahul tied the sticks at what angles to each other?
a) 30°
b) 60°
c) 90°
d) 60°

Answer: C

Question. Which is the correct similarity criteria applicable for smaller triangles at the upper part of this kite?
a) RHS
b) SAS
c) SSA
d) AAS

Answer: B

iii. Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles are in the ratio,
a) 2:3
b) 4:9
c) 81:16
d) 16:81

Answer: B

Question. In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called as,
a) Pythagoras theorem
b) Thales theorem
c) Converse of Thales theorem
d) Converse of Pythagoras theorem

Answer: D

Question. What is the area of the kite, formed by two perpendicular sticks of length 6 cm and 8 cm?
a) 48 cm2
b) 14 cm2
c) 24 cm2
d) 96 cm2

Answer: C

3. Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles. The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground

Question. What is the height of the tower?
a) 20m
b) 50m
c) 100m
d) 200m

Answer: C

Question. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?
a) 75m
b) 50m
c) 45m
d) 60m

Answer: D

Question. What is the height of Ajay’s house?
a) 30m
b) 40m
c) 50m
d) 20m

Answer: B

Question. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house?
a) 16m
b) 32m
c) 20m
d) 8m

Answer: A

Question. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house?
a) 15m
b) 32m
c) 16m
d) 8m

Answer: D

4. Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below. To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12m, connecting C to point D at a distance of 40m from point C and the connecting D to the point A which is are a distance of 30m from D such that ∠ADC=900.

Question. Which property of geometry will be used to find the distance AC?
a) Similarity of triangles
b) Thales Theorem
c) Pythagoras Theorem
d) Area of similar triangles

Answer: C

Question. What is the distance AC?
a) 50m
b) 12m
c) 100m
d) 70m

Answer: A

Question. Which is the following does not form a Pythagoras triplet?
a) (7,24,25)
b) (15,8,17)
c) (5,12,13)
d) (21,20,28)

Answer: D

Question. Find the length AB?
a) 12m
b) 38m
c) 50m
d) 100m

Answer: B

Question. Find the length of the rope used.
a) 120m
b) 70m
c) 82m
d) 22m

Answer: C

5. A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor Scale factor= length in image / corresponding length in object If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200
This means that a length of 1 cm on the photograph above corresponds to a length of 200cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.

Question. If the length of the model is 11cm, then the overall length of the engine in the photograph above, including the couplings(mechanism used to connect) is:
a) 22cm
b) 220cm
c) 220m
d) 22m

Answer: D

Question. What will affect the similarity of any two polygons?
a) They are flipped horizontally
b) They are dilated by a scale factor
c) They are translated down
d) They are not the mirror image of one another.

Answer: D

Question. What is the actual width of the door if the width of the door in photograph is 0.35cm?
a) 0.7m
b) 0.7cm
c) 0.07cm
d) 0.07m

Answer: A

Question. If two similar triangles have a scale factor 5:3 which statement regarding the two triangles is true?
a) The ratio of their perimeters is 15:1
b) Their altitudes have a ratio 25:15
c) Their medians have a ratio 10:4
d) Their angle bisectors have a ratio 11:5

Answer: B

Question. The length of AB in the given figure:

a) 8cm
b) 6cm
c) 4cm
d) 10cm

Answer: C