M l aggarwal understanding icse mathematics class 9 Solutions for Chapter 10 triangles

Exercises in Chapter 10 triangles Grade 9

Triangles Exercise 10.1

Triangles Exercise 10.2

Triangles Exercise 10.3

Triangles Exercise 10.4

Questions in Triangles Exercise 10.1

It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR? Why?

In the given figure, AB=AC and AP=AQ. Prove that

(i) ∆APC ≅ ∆AQB

(ii) CP = BQ

(iii) ∠APC = ∠AQB.

In the given figure, AB = AC, P, and Q are points on BA and CA respectively such that

AP = AQ. Prove that

(i) ∆APC ≅ ∆AQB

(ii) CP = BQ

(iii) ∠ACP = ∠ABQ.

In the given figure, AD = BC and BD = AC. Prove that :

∠ADB = ∠BCA and ∠DAB = ∠CBA

In the given figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA.

Prove that

(i) ∆ABD ≅ ∆BAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

In the given figure, AB = DC and AB || DC. Prove that AD = BC.

In the given figure. AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.

In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that

(i) ∆ACE ≅ ∆DBF

(ii) AE = DF.

Questions in Triangles Exercise 10.2

In triangles ABC and PQR, ∠A= ∠Q and ∠B = ∠R. Which side of APQR should be

equal to side AB of AABC so that the two triangles are congruent? Give the reason for your

answer.

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of APQR should be

equal to side BC of AABC so that the two triangles are congruent? Give the reason for your

answer.

“If two angles and a side of one triangle are equal to two angles and a side of

another triangle, then the two triangles must be congruent”. Is the statement true?

Why?

In the given figure, AD is median of ∆ABC, BM and CN are perpendiculars drawn

from B and C respectively on AD and AD produced. Prove that BM = CN.

In the given figure, BM and DN are perpendiculars to the line segment AC. If BM =

DN, prove that AC bisects BD.

In the given figure, l and m are two parallel lines intersected by another pair of

parallel lines p and q. Show that ∆ABC ≅ ∆CDA.

In the given figure, two lines AB and CD intersect each other at the point O such

that BC || DA and BC = DA. Show that O is the mid-point of both the line segments AB

and CD.

Questions in Triangles Exercise 10.3

ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Show that every equiangular triangle is equilateral.

In the following diagrams, find the value of x:

(a) In the figure (1) given below, ABC is an equilateral triangle. Base BC is produced

to E, such that BC’= CE. Calculate ∠ACE and ∠AEC.

(b) In the figure (2) given below, prove that ∠ BAD: ∠ ADB = 3: 1.

In the given figure, AD, BE, and CF arc altitudes of ∆ABC. If AD = BE = CF, prove that

ABC is an equilateral triangle.

In the given figure, D is the mid-point of BC, DE and DF are perpendiculars to AB and AC

respectively such that DE = DF. Prove that ABC is an isosceles triangle.

Questions in Triangles Exercise 10.4

In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? Give reason

for your answer.

Show that in a right-angled triangle, the hypotenuse is the longest side.

PQR is a right angle triangle at Q and PQ: QR = 3:2. Which is the least angle?

In ∆ ABC, AB = 8 cm, BC = 5.6 cm and CA = 6.5 cm. Which is

(i) the greatest angle ?

(ii) the smallest angle?

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Chapters in this book

Rational and Irrational Numbers

Compound Interest

Expansions

Factorization

Simultaneous Linear Equations

Problems on Simultaneous Linear Equations

Quadratic Equations

Indices

Logarithms

Triangles

Mid Point Theorem

Pythagoras Theorem

Rectilinear Figures

Theorems on Area

Circle

Mensuration

Trigonometric Ratios

Trigonometric Ratios and Standard Angles

Coordinate Geometry

Statistics