CBSE Class 10 Maths HOTs Similar Triangles Set 02

Say True (T) or False (F).

Question. Congruent shapes are never similar.
Answer: F

Question. Similar figures are always congruent.
Answer: F

Question. Ratio of areas of two similar triangles is same as ratio of squares of their perimeters.
Answer: T

Question. Circles of different radii are always similar.
Answer: T

Question. \( \Delta ABC \) with sides 5, 12, 13 is obtuse angled triangle.
Answer: F

Question. Another name of B.P.T is Thales theorem.
Answer: T

Question. Pythagoras theorem is also known as Budhain theorem.
Answer: T

Question. AAA. is not a condition of similarity.
Answer: F

Question. Pythagoras theorem is not applicable in right angled triangles.
Answer: F

Question. Ratio of areas of a triangle formed by joining mid points of sides of triangle to original triangle is 1 : 4.
Answer: T

Question. Two equilateral triangles of different length of sides are congruent to each other.
Answer: F

Question. In an equilateral triangle \( ABC \), \( AD \perp BC \) then \( AD^2 = \frac{1}{4} BC^2 \).
Answer: F

Question. In a right angled triangle \( ABC \) right angled at \( A \), \( AD \perp BC \) then \( BC^2 = AD \times AB \).
Answer: F

Question. Two similar triangles of equal areas are congruent.
Answer: T

Question. If two polygons are similar then their sides are proportional.
Answer: T

Question. Two rhombus having same length of side are always similar.
Answer: F

Question. R.H.S. is one of the condition of similarity.
Answer: F

Question. Ratio of heights of two objects is equal to ratio of the length of their corresponding shadow at same time.
Answer: T

Question. If diagonals of a quadrilateral are proportional then it is not a Trapezium.
Answer: F

Fill in the Blank.

Question. If \( \Delta ABC \sim \Delta PQR \) then \( \angle B = \) ________.
Answer: \( \angle Q \)

Question. If \( \Delta FED \sim \Delta STU \) the \( \frac{EF}{ST} = \) ________.
Answer: \( \frac{ED}{TU} \) or \( \frac{FD}{SU} \)

Question. If \( \Delta ABC \sim \Delta PQR \) with \( \frac{BC}{QR} = \frac{1}{4} \). Then \( \frac{ar \Delta PRQ}{ar \Delta BCA} = \) ________.
Answer: 1 : 16

Question. If two triangles are similar such that ratio of their areas is 25 : 361 then ratio of corresponding medians is ________.
Answer: 5 : 19

Question. In \( \Delta ABC \) and \( \Delta DEF \), \( \angle B = \angle E \), \( \angle F = \angle C \) and \( AB = 2DE \) two triangles are ________.
Answer: Similar

Question. Diagonals of a trapezium PQRS intersect each other at the point O, and \( PQ = 3RS \). Ratio of areas of triangles POQ and ROS is ________.
Answer: 9 : 1

Question. In a triangle PQR, N is point on PR such that \( QN \perp PR \), also \( PN \cdot NR = QN^2 \). Then \( \angle PQR = \) ________.
Answer: 90°

Question. Ratio of perimeters of two similar triangles is same as ratio of corresponding ________.
Answer: sides or medians, altitudes or angle bisectors

Question. If S is a point on side PQ of a \( \Delta PQR \) such that \( PS = QS = RS \) then \( PR^2 + QR^2 = \) ________.
Answer: \( PQ^2 \)

Question. If D & E are points of trisection of sides AB and AC of \( \Delta ABC \) then \( DE = \) ________.
Answer: \( BC/3 \)

MCQs with more than one correct options.

Question. Two triangles can be similar by ............... condition of similarity.
(a) SSS
(b) RHS
(c) AAA
(d) ASA
Answer: (a) SSS, (c) AAA

Question. Ratio of sides of two similar triangles is same as the ratio of its corresponding.
(a) Medians
(b) Altitudes
(c) Angle bisectors
(d) Areas
Answer: (a) Medians, (b) Altitudes, (c) Angle bisectors

Question. Two circles of same radii are always:
(a) Similar
(b) Unequal
(c) Congruent
(d) Concentric
Answer: (a) Similar, (c) Congruent

Question. Ratio of areas of two similar triangles is same as ratio of squares of their corresponding.
(a) Medians
(b) Altitudes
(c) Perimeters
(d) angle bisectors
(e) sides
Answer: (a) Medians, (b) Altitudes, (c) Perimeters, (d) angle bisectors

Question. In a right angled triangle ABC right angled at B, \( BD \perp AC \) then which of following are true.
(a) \( \Delta ABC \sim \Delta ADB \)
(b) \( \Delta ABC \sim \Delta BDC \)
(c) \( \Delta ADB \sim \Delta BDC \)
(d) \( \Delta ABC \sim \Delta DBC \)
Answer: (a) \( \Delta ABC \sim \Delta ADB \), (b) \( \Delta ABC \sim \Delta BDC \), (c) \( \Delta ADB \sim \Delta BDC \)

Question. In a \( \Delta ABC \), D & E are points on sides AB & AC respectively such that \( DE \parallel BC \) then which of followings results may be used for making \( DE \parallel BC \)
(a) \( \frac{AD}{AB} = \frac{AE}{EC} \)
(b) \( \frac{AB}{BD} = \frac{AC}{EC} \)
(c) \( \frac{AD}{AB} = \frac{AE}{AC} \)
(d) \( \frac{AD}{DE} = \frac{AE}{BC} \)
Answer: (b) \( \frac{AB}{BD} = \frac{AC}{EC} \), (c) \( \frac{AD}{AB} = \frac{AE}{AC} \)

Question. Diagonal of parallelogram separates it into two triangles which are :
(a) Similar
(b) Congruent
(c) Equal in area
(d) None of the options
Answer: (a) Similar, (b) Congruent, (c) Equal in area

Question. Two chords AB and CD intersects each other at P (Inside or out side) then which of the results are true
(a) \( \Delta APC \cong \Delta DPB \)
(b) \( AP \cdot DP = PB \cdot CP \)
(c) \( AP \cdot PB = CP \cdot DP \)
(d) \( \Delta APC \sim \Delta DPB \)
Answer: (c) \( AP \cdot PB = CP \cdot DP \), (d) \( \Delta APC \sim \Delta DPB \)

Question. In a \( \Delta PQR \), \( PQ = PR \), S and T are mid-points on sides PQ & PR respectively then which of the following about triangle PST is not true.
(a) \( \Delta PQR \) is isosceles
(b) \( \Delta PQR \) will be always equilateral
(c) \( \Delta PQR \) will be always right angled
(d) Can not say
Answer: (b) \( \Delta PQR \) will be always equilateral, (c) \( \Delta PQR \) will be always right angled

Question. In an equilateral \( \Delta ABC \), D is a point on side BC such that \( BD = \frac{1}{3} BC \) then which of following can not be equal to \( 9 AD^2 \).
(a) \( 7AB^2 \)
(b) \( 7AC^2 \)
(c) \( 11BC^2 \)
(d) Can not say
Answer: (b) \( 7AC^2 \), (c) \( 11BC^2 \)