CBSE Class 10 Mathematics Triangles Worksheet Set H

Triangles

Key Points

Similar Figures: Two figures having similar shapes (size may or may not same), called Similar figures.

Examples: (a) & (b) & (c) &

A pair of Circles A pair of squares A pair of Equ. Triangles

- Pairs of all regular polygons, containing equal number of sides are examples of Similar Figures.

- Similar Triangles: Two Triangles are said to be similar if

(a) Their corresponding angles are equal ( also called Equiangular Triangles)

(b) Ratio of their corresponding sides are equal/proportional

- All congruent figures are similar but similar figures may /may not congruent

- Conditions for similarity of two Triangles

(a) AAA criterion/A-A corollary

(b) SAS similarity criterion

(c) SSS similarity criterion (where ‘S’ stands for ratio of corresponding sides of two Triangles)

Important Theorems of the topicTriangles

(a) Basic Proportionality Theorem (B.P.T.)/Thale’s Theorem

(b) Converse of B.P.T.

(c) Area related theorem of Similar Triangles

(d) Pythagoras Theorem

(e) Converse of Pythagoras Theorem

Level I

(1) In the figure XY ∕∕ QR , PQ/ XQ = 7/3 and PR =6.3cm then find YR

(2) If ΔABC ~ Δ DEF and their areas be 64cm2& 121cm2 respectively , then find BC if EF =15.4 cm

(3) ABC is an isosceles Δ ,right angled at C then prove that AB2 = 2AC2

(4) If ΔABC ~ Δ DEF, ∟A=460, ∟E= 620 then the measure of ∟C=720. Is it true? Give reason.

(5) The ratio of the corresponding sides of two similar triangles is 16:25 then find the ratio of their perimeters.

(6) A man goes 24 km in due east and then He goes 10 km in due north. How far is He from the starting Point?

(7) The length of the diagonals of a rhombus is 16cm & 12cm respectively then find the perimeter of the rhombus.

(8) In the figure LM ∕∕CB and LN ∕∕ CD then prove that AM/AB = AN /AD

(9) Which one is the sides of a right angled triangles among the following (a) 6cm,8cm & 11cm (b) 3cm,4cm & 6cm (c) 5cm , 12cm & 13cm

Level II

(1) In the figure ABD is a triangle right angled at A and AC is perpendicular to BD then show that AC2= BC x DC

(2) Two poles of height 10m & 15 m stand vertically on a plane ground. If the distance between their feet is 5√3m then find the distance between their tops.

(3) D & E are the points on the sides AB & AC of ΔABC, as shown in the figure. If ∟B = ∟AED then show that ΔABC ~ΔAED

(4) In the adjoining figure AB ∕∕ DC and diagonal AC & BD intersect at point O. If AO = (3x-1)cm , OB= (2x+1)cm, OC=(5x-3 )cm and OD=( 6x-5)cm then find the value of x.

(5) In the figure D &E trisect BC. Prove that 8AE2= 3AC2+ 5AD2

(6) In the figure OA/OC = OD /OB then prove that ∟A= ∟C

Question. Can cos θ = 5/4 be possible?
Answer: No 

Question. If θ = 45°, find the value of sec² θ.
Answer: 2 

Question. If θ is a positive acute angle such that sec θ = cosec60°, then find the value of 2 cos² θ-1.
Answer: 1/4

 Question. Find the value of 9 sec² A – 9 tan²A.
Answer: -9

Question. If ar ΔABC = 1/4 ar ΔDEF Find AB/DE
Answer: 1/2 

Question. Find the value of sin65° – cos25° without using tables.
Answer: 0

Question. In ΔABC, if 2AB²=AC², Find ∠ B.
Answer: 90^o 

Question. If 2 sin X/2 – 1 = 0, find the value of x.
Answer: 90⁰

Question. If sec 5A = cosec(A – 36°), find the value of A.
Answer: 21⁰ 

Question. ΔADE ˜ Δ ABC , if DE=4cm, BC=8cm and ar(ΔADE)=25sq cm. Find the area of ΔABC.
Answer: 100

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