Assignments for Class 9 Mathematics Triangles have been developed for Standard 9 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 9 Mathematics Triangles from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 9 Mathematics Triangles. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Triangles book and get good marks in class 9 exams.

**Key Concepts** for Class 9 Mathematics Triangles

**• Triangle –** A closed figure formed by three intersecting lines is called a triangle. A triangle has three sides, three angles and three vertices.**• Congruent figures –** Congruent means equal in all respects or figures whose shapes and sizes are both the same for example, two circles of the same radii are congruent. Also two squares of the same sides are congruent.**•** **Congruent Triangles –** two triangles are congruent if and only if one of them can be made to superpose on the other, so as to cover it exactly.**•** If two triangles ABC and PQR are congruent under the correspondence A ↔ p, B ↔ and C ↔ R then symbolically, it is expressed as ΔABC ≅ PQR

**•** In congruent triangles corresponding parts are equal and we write ‘CPCT’ for corresponding parts of congruent triangles.

• SAS congruency rule – Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. For example ΔABC and ΔPQR as shown in the figure satisfy SAS congruent criterion.

**• ASA Congruence Rule –** Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. For examples ΔABC and ΔDEF shown below satisfy ASA congruence criterion.

**•****AAS Congruence Rule – **Two triangle are congruent if any two pairs of angles and one pair of corresponding sides are equal for example ΔABC and ΔDEF shown below satisfy AAS congruence criterion.

** •** AAS criterion for congruence of triangles is a particular case of ASA criterion.

**•****Isosceles Triangle –**A triangle in which two sides are equal is called an isosceles triangle. For example ΔABC shown below is an isosceles triangle with AB = AC.

** •** Angle opposite to equal sides of a triangle are equal.

**•** Sides opposite to equal angles of a triangle are equal.**•** Each angle of an equilateral triangle is 60^{0}.**•** **SSS congruence Rule –** If three sides of one triangle are equal to the three sides of another triangle then the two triangles are congruent for example ΔABC and ΔDEF as shown in the figure satisfy SSS congruence criterion.

**• RHS Congruence Rule **– If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle then the two triangle are congruent. For example ΔABC and PQR shown below satisfy RHS congruence criterion.

**RHS stands for right angle – Hypotenuse side.**

**•** A point equidistant from two given points lies on the perpendicular bisector of the line segment joining the two points and its converse.**•** A point equidistant from two intersecting lines lies on the bisectors of the angles formed by the two lines.**•** In a triangle, angle opposite to the longer side is larger (greater)**•** In a triangle, side opposite to the large (greater) angle is longer.**•** Sum of any two sides of a triangle is greater than the third side.

**Class 9 Mathematics Triangles** Assignments

**Class 9 Mathematics Triangles Important Questions and Answers**

**Question. In Δ PQR, if ∠R > ∠Q then**

(a) QR > PR

(b) PQ > PR

(c) PQ < PR

(d) QR < PR

**Ans.**

b

**Question.** In the given figure, if OA=OB, OD=OC then Δ AOD ≅ Δ BOC by congruence rule.

(a) SSS

(b) ASA

(c) SAS

(d) RHS

**Ans.**

c

**Question.** Which of the following is not a criterion for congruence of triangles?

(a) SAS

(b) SSA

(c) ASA

(d) SSS

**Ans.**

b

**Question.** In the figure if PQ=PR and ∠P = 80^{0}, then measure of Q is

(a) 100^{0}

(b) 50^{0}

(c) 80^{0}

(d) 40^{0}

**Ans.**

b

**Question.** In the figure, if ΔABC ≅ ΔCDA, the property of congruence is

(a) SSS

(b) SAS

(c) RHS

(d) ASA

**Ans.**

c

**Question.** If ΔPQR ≅ ΔEFD, then, ∠E =

(a) ∠P

(b) ∠Q

(c) ∠R

(d) None of these

**Ans.**

a

**Question.** ΔABC ≅ ΔDEF and if AB = 3 = DE and BC = EF = 4 then necessary condition is

(a) ∠A = ∠D

(b) ∠B = ∠E

(c) ∠C = ∠F

(d) CA = FD

**Ans.**

b

**Question.** It is not possible to construct a triangle when its sides are

(a) 8.3cm, 3.4cm, 6.1cm

(b) 5.4cm, 2.3cm, 3.1cm

(c) 6cm, 7cm, 10cm

(d) 3cm, 5cm, 5cm

**Ans.**

b

**Question.** If AB=QR, BC=PR and CA=PQ then

(a) ΔABC ≅ ΔPQR

(b) ΔBAC ≅ ΔPRQ

(c) ΔBAC ≅ ΔRPQ

(d) ΔPQR ≅ ΔBCA

**Ans.**

b

**Question.** In a , ΔABC, if AB=AC and BC is produced to D such that ∠ACD = 1000 then ∠A

(a) 20^{0}

(b) 40^{0}

(c) 60^{0}

(d) 80^{0}

**Ans.**

a

**Question.** In the figure ΔABC ≅ ΔADC if ∠ACB = 25^{0} and ∠B = 125^{0}, then ∠CAD is

(a) 25^{0}

(b) 650

(c) 30^{0}

(d) 75^{0}

**Ans.**

c

**Question.** In the figure AB=AC and ∠ACD = 120^{0} find ∠A

**Ans.**

60^{0}

**Question.** If ΔPQR ≅ ΔEFD, then ED =

(a) PQ

(b) QR

(c) PR

(d) None of these

**Ans.**

c

**Question.** In a ΔABC if ∠A = 45^{0} and ∠B = 70^{0} determine the shortest and largest sides of the triangle

**Ans.**

BC, AC

## Assignments for Class 9 Mathematics Triangles as per CBSE NCERT pattern

All students studying in Grade 9 Mathematics Triangles should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Triangles exam for standard 9. We have made sure that all topics given in your textbook for Mathematics Triangles which is suggested in Class 9 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

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- You will be able to understand the type of questions which are expected in your Mathematics Triangles class test
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