#### Chapters

Chapter 2: Profit , Loss and Discount

Chapter 3: Compound Interest

Chapter 4: Expansions

Chapter 5: Factorisation

Chapter 6: Changing the subject of a formula

Chapter 7: Linear Equations

Chapter 8: Simultaneous Linear Equations

Chapter 9: Indices

Chapter 10: Logarithms

Chapter 11: Triangles and their congruency

Chapter 12: Isosceles Triangle

Chapter 13: Inequalities in Triangles

Chapter 14: Constructions of Triangles

Chapter 15: Mid-point and Intercept Theorems

Chapter 16: Similarity

Chapter 17: Pythagoras Theorem

Chapter 18: Rectilinear Figures

Chapter 19: Quadrilaterals

Chapter 20: Constructions of Quadrilaterals

Chapter 21: Areas Theorems on Parallelograms

Chapter 22: Statistics

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Perimeter and Area

Chapter 25: Surface Areas and Volume of Solids

Chapter 26: Trigonometrical Ratios

Chapter 27: Trigonometrical Ratios of Standard Angles

Chapter 28: Coordinate Geometry

## Chapter 11: Triangles and their congruency

### Frank solutions for Class 9 Maths ICSE Chapter 11 Triangles and their congruency Exercise 11.1

In the given figure, ∠Q: ∠R = 1: 2. Find:

a. ∠Q

b. ∠R

The exterior angles, obtained on producing the side of a triangle both ways, are 100° and 120°. Find all the angles of the triangle.

Use the given figure to find the value of x in terms of y. Calculate x, if y = 15°.

In a triangle PQR, ∠P + ∠Q = 130° and ∠P + ∠R = 120°. Calculate each angle of the triangle.

The angles of a triangle are (x + 10)°, (x + 30)° and (x - 10)°. Find the value of 'x'. Also, find the measure of each angle of the triangle.

Use the given figure to find the value of y in terms of p, q and r.

In the figure given below, if RS is parallel to PQ, then find the value of ∠y.

In a triangle PQR, the internal bisectors of angles Q and R meet at A and the external bisectors of the angles Q and R meet at B. Prove that: ∠QAR + ∠QBR = 180°.

Use the given figure to show that: ∠p + ∠q + ∠r = 360°.

In a triangle ABC. If D is a point on BC such that ∠CAD = ∠B, then prove that: ∠ADC = ∠BAC.

In a triangle ABC, if the bisectors of angles ABC and ACB meet at M then prove that: ∠BMC = 90° + `(1)/(2)` ∠A.

If bisectors of angles A and D of a quadrilateral ABCD meet at 0, then show that ∠B + ∠C = 2 ∠AOD

If each angle of a triangle is less than the sum of the other two angles of it; prove that the triangle is acute-angled.

If the angles of a triangle are in the ratio 2: 4: 6; show that the triangle is a right-angled triangle.

In a triangle, the sum of two angles is 139° and their difference is 5°; find each angle of the triangle.

In a right-angled triangle ABC, ∠B = 90°. If BA and BC produced to the points P and Q respectively, find the value of ∠PAC + ∠QCA.

### Frank solutions for Class 9 Maths ICSE Chapter 11 Triangles and their congruency Exercise 11.2

Which of the following pairs of triangles are congruent? Give reasons

ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);

ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).

Which of the following pairs of triangles are congruent? Give reasons

ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);

ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).

Which of the following pairs of triangles are congruent? Give reasons

ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);

ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).

Which of the following pairs of triangles are congruent? Give reasons

ΔABC;(∠B = 70°,BC = 6cm,∠C = 50°);

ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).

Which of the following pairs of triangles are congruent? Give reasons

ΔABC;(∠B = 90°,BC = 6cm,AB = 8cm);

ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).

A is any point in the angle PQR such that the perpendiculars drawn from A on PQ and QR are equal. Prove that ∠AQP = ∠AQR.

In the given figure P is a midpoint of chord AB of the circle O. prove that OP ^ AB.

In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.

In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.

In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:

a. DABD andDECD are congruent.

b. AB = EC

c. AB is parallel to EC

In the figure, ∠CPD = ∠BPD and AD is the bisector of ∠BAC. Prove that ΔCAP ≅ ΔBAP and CP = BP.

In the figure, BC = CE and ∠1 = ∠2. Prove that ΔGCB ≅ ΔDCE.

In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.Prove that BO = CO and the ray AO is the bisector of angle BAC.

In the figure, AB = EF, BC = DE, AB and FE are perpendiculars on BE. Prove that ΔABD ≅ ΔFEC

In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.

In ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.

In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.

AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.

In ΔABC, X and Y are two points on AB and AC such that AX = AY. If AB = AC, prove that CX = BY.

If the perpendicular bisector of the sides of a triangle PQR meet at I, then prove that the line joining from P, Q, R to I are equal.

In the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.

In the given figure ABCD is a parallelogram, AB is Produced to L and E is a midpoint of BC. Show that:

a. DDCE ≅ DLDE

b. AB = BL

c. DC = `"AL"/(2)`

In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.

In the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the mid-point of the line segments AB and PQ.

ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.

Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.

Prove that in an isosceles triangle the altitude from the vertex will bisect the base.

In ΔABC, AB = AC. D is a point in the interior of the triangle such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of ΔABC.

O is any point in the ΔABC such that the perpendicular drawn from O on AB and AC are equal. Prove that OA is the bisector of ∠BAC.

In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.

ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.

Prove that

(i) BG = CH

(ii) AG = AH

In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.

Two right-angled triangles ABC and ADC have the same base AC. If BC = DC, prove that AC bisects ∠BCD.

PQRS is a quadrilateral and T and U are points on PS and RS respectively such that PQ = RQ, ∠PQT = ∠RQU and ∠TQS = ∠UQS. Prove that QT = QU.

In the given figure, AB = DB and AC = DC. Find the values of x and y.

## Chapter 11: Triangles and their congruency

## Frank solutions for Class 9 Maths ICSE chapter 11 - Triangles and their congruency

Frank solutions for Class 9 Maths ICSE chapter 11 (Triangles and their congruency) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Class 9 Maths ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Maths ICSE chapter 11 Triangles and their congruency are Relation Between Sides and Angles of Triangle, Important Terms of Triangle, Congruence of Triangles, Criteria for Congruence of Triangles, Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle.

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