#### Chapters

Chapter 2: Compound Interest (Without using formula)

Chapter 3: Compound Interest (Using Formula)

Chapter 4: Expansions (Including Substitution)

Chapter 5: Factorisation

Chapter 6: Simultaneous (Linear) Equations (Including Problems)

Chapter 7: Indices (Exponents)

Chapter 8: Logarithms

Chapter 9: Triangles [Congruency in Triangles]

Chapter 10: Isosceles Triangles

Chapter 11: Inequalities

Chapter 12: Mid-point and Its Converse [ Including Intercept Theorem]

Chapter 13: Pythagoras Theorem [Proof and Simple Applications with Converse]

Chapter 14: Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]

Chapter 15: Construction of Polygons (Using ruler and compass only)

Chapter 16: Area Theorems [Proof and Use]

Chapter 17: Circle

Chapter 18: Statistics

Chapter 19: Mean and Median (For Ungrouped Data Only)

Chapter 20: Area and Perimeter of Plane Figures

Chapter 21: Solids [Surface Area and Volume of 3-D Solids]

Chapter 22: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]

Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]

Chapter 24: Solution of Right Triangles [Simple 2-D Problems Involving One Right-angled Triangle]

Chapter 25: Complementary Angles

Chapter 26: Co-ordinate Geometry

Chapter 27: Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)

Chapter 28: Distance Formula

## Chapter 9: Triangles [Congruency in Triangles]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 9 Triangles [Congruency in Triangles] Exercise 9 (A) [Pages 122 - 123]

**If the following pair of the triangle is congruent? state the condition of congruency : **

In Δ ABC and Δ DEF, AB = DE, BC = EF and ∠ B = ∠ E.

**If the following pair of the triangle is congruent? state the condition of congruency : **

In ΔABC and ΔDEF, ∠B = ∠E = 90^{o}; AC = DF and BC = EF.

**If the following pair of the triangle is congruent? state the condition of congruency: **

In ΔABC and ΔQRP, AB = QR, ∠B = ∠R and ∠C = P.

**If the following pair of the triangle is congruent? state the condition of congruency: **

In ΔABC and ΔPQR, AB = PQ, AB = PQ, and BC = QR.

**If the following pair of the triangle is congruent? state the condition of congruency: **

In ΔADC and ΔPQR, BC = QR, ∠A = 90^{o}, ∠C = ∠R = 40^{o} and ∠Q = 50^{o}.

**The given figure shows a circle with center O. P is mid-point of chord AB.**

Show that OP is perpendicular to AB.

**The following figure shows a circle with center O.**

If OP is perpendicular to AB, prove that AP = BP.

**In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that :**(i) ΔABD and ΔECD are congruent.

(ii) AB = CE.

(iii) AB is parallel to EC

A triangle ABC has ∠B = ∠C.Prove that: The perpendiculars from the mid-point of BC to AB and AC are equal.

A triangle ABC has B = C.

Prove that: The perpendicu...lars from B and C to the opposite sides are equal.

**The perpendicular bisectors of the sides of a triangle ABC meet at I.**

Prove that: IA = IB = IC.

A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that: QA = QB.

If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.Prove that:

(i) ΔDCE ≅ ΔLBE

(ii) AB = BL.

(iii) AL = 2DC

**In the given figure, AB = DB and Ac = DC.**

If ∠ ABD = 58

^{o},

∠ DBC = (2x - 4)

^{o},

∠ ACB = y + 15

^{o}and

∠ DCB = 63

^{o}; find the values of x and y.

**In the given figure: AB//FD, AC//GE and BD = CE; **prove that: (i) BG = DF (ii) CF = EG

In âˆ†ABC, AB = AC. Show that the altitude AD is median also.

**In the following figure, BL = CM.**

Prove that AD is a median of triangle ABC.

**In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.**Prove that: BD = CD

**In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.**Prove that : ED = EF

**Use the information in the given figure to prove :**(i) AB = FE

(ii) BD = CF

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 9 Triangles [Congruency in Triangles] Exercise 9 (B) [Pages 125 - 126]

**On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. **Prove that: (i) ∠CAD = ∠BAE

(ii) CD = BE

**In the following diagram, ABCD is a square and APB is an equilateral triangle.**(i) Prove that: ΔAPD≅ ΔBPC

(ii) Find the angles of ΔDPC.

**In the following diagram, ABCD is a square and APB is an equilateral triangle.**(i) Prove that: ΔAPD ≅ ΔBPC

(ii) Find the angles of ΔDPC.

In the figure, given below, triangle ABC is right-angled at B. ABPQ and ACRS are squares.

Prove that:

(i) ΔACQ and ΔASB are congruent.

(ii) CQ = BS.

**In a ΔABC, BD is the median to the side AC, BD is produced to E such that BD = DE.**

Prove that: AE is parallel to BC.

**In the adjoining figure, OX and RX are the bisectors of the angles Q and R respectively of the triangle PQR.If XS ⊥ QR and XT ⊥ PQ ;**

prove that: (i) ΔXTQ ≅ ΔXSQ.

(ii) PX bisects angle P.

**In the parallelogram ABCD, the angles A and C are obtuse. Points X and Y are taken on the diagonal BD such that the angles XAD and YCB are right angles.**Prove that: XA = YC.

**ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such produced to E and F respectively, such that AB = BE and AD = DF.**

Prove that: ΔBEC ≅ ΔDCF.

**In the following figures, the sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and median PS of the triangle PQR. **Prove that ΔABC and ΔPQR are congruent.

In the following diagram, AP and BQ are equal and parallel to each other.

Prove that:

(i) ΔAOP≅ ΔBOQ.

(ii) AB and PQ bisect each other.

**In the following figure, OA = OC and AB = BC.**

Prove that:

(i) ∠AOB = 90o

(ii) ΔAOD ≅ ΔCOD

(iii) AD = CD

**The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.**

Prove that: (i) AM = AN (ii) ΔAMC ≅ ΔANB

**The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.**

Prove that: (i) BN = CM (ii) ΔBMC≅ΔCNB

In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB.

Prove that: AD = CE.

**PQRS is a parallelogram. L and M are points on PQ and SR respectively such that PL = MR.**

Show that LM and QS bisect each other.

**In the following figure, ABC is an equilateral triangle in which QP is parallel to AC. Side AC is produced up to point R so that CR = BP.**

Prove that QR bisects PC.**Hint:** ( Show that âˆ† QBP is equilateral

⇒ BP = PQ, but BP = CR

⇒ PQ = CR ⇒ âˆ† QPM ≅ âˆ† RCM ).

**In the following figure, ∠A = ∠C and AB = BC.**

Prove that ΔABD ≅ ΔCBE.

AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides of AB prove that CD bisects AB.

**In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.**

Prove that : (i) BO = CO

(ii) AO bisects angle BAC.

**In the following figure, AB = EF, BC = DE and ∠B = ∠E = 90°.**

Prove that AD = FC.

A point O is taken inside a rhombus ABCD such that its distance from the vertices B and D are equal. Show that AOC is a straight line.

In quadrilateral ABCD, AD = BC and BD = CA.

Prove that:

(i) ∠ADB = ∠BCA

(ii) ∠DAB = ∠CBA

## Chapter 9: Triangles [Congruency in Triangles]

## Selina solutions for Concise Mathematics Class 9 ICSE chapter 9 - Triangles [Congruency in Triangles]

Selina solutions for Concise Mathematics Class 9 ICSE chapter 9 (Triangles [Congruency in Triangles]) 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 Concise Mathematics Class 9 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 9 ICSE chapter 9 Triangles [Congruency in Triangles] 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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