CBSE Class 10 Maths (Basic) 2023 · Paper 430/4/1 · Question 38

Triangles 4 marks Hard

Observe the figures given below carefully and answer the questions. Figure A shows two quadrilaterals

A B C D

(with

A B = 1.2

cm,

B C = 2.5

cm,

C D = 2.4

cm,

D A = 2

cm and marked angles) and

P QR S

(with

P Q = 2.4

cm,

QR = 5

cm,

R S = 4.8

cm,

S P = 4

cm and the same marked angles). Figure B shows two squares of sides

3.5

cm and

3

cm. Figure C shows two triangles

A B C

and

P QR

with sides

2

cm,

3

cm and

4.5

cm each.

Figure A: two trapezia with equal angles and sides in ratio 1:2.

Figure B: two squares of sides 3.5 cm and 3 cm.

Figure C: two triangles with sides 2, 3 and 4.5 cm each.

(i)Name the figure(s) wherein two figures are similar.[1]
(ii)Name the figure(s) wherein the figures are congruent.[1]
(iii)(a)Prove that congruent triangles are also similar but not the converse.[2]
(iii)(b)What more is least needed for two similar triangles to be congruent?[2]

Answer

(i) Figures A, B and C all show similar pairs — A with scale factor

2

, B because any two squares are similar, C because congruent triangles are similar with ratio

1

; (ii) Only Figure C shows congruent figures (SSS); (iii)(a) Congruent triangles have equal angles and all side ratios equal to

1

, so they are similar; the converse fails — the squares in B, or equilateral triangles of sides

2

cm and

4

cm, are similar but not congruent; (iii)(b) Equality of any one pair of corresponding sides (scale factor

1

) is the least that is needed.

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