NCERT Mathematics Class 9 Exemplar Ch 7 Triangles Part 3

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Exercise 7.2

Q.1. In triangles ABC and PQR, and . Which side of ∆ PQR should be equal to side AB of ∆ ABC so that the two triangles are congruent? Give reason for your answer.

Answer: QR; they will be congruent by ASA.

Q.2. In triangles ABC and PQR, . Which side of ∆ PQR should be equal to side BC of ∆ ABC so that the two triangles are congruent? Give reason for your answer.

Answer: RP; they will be congruent by AAS.

Q.3. If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

Answer: No; Angles must be included angles.

Q.4. “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?

Answer: No; Sides must be corresponding sides.

Q.5. Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.

Answer: No; Sum of the two sides = the third side.

Q.6. 6.It is given that. Is it true to say that? Why?

Answer: No;.

Q.7. If , then is it true to say that ? Give reason for your answer.

Answer: Yes; they are corresponding sides.

Q.8. In ∆ PQR, and. Which side of this triangle is the longest? Give reason for your answer.

Answer: PR; Side opposite the greater angle is longer.

Q.9. AD is a median of the triangle ABC. Is it true that ? Give reason for your answer.

Answer: Yes; and .

Q.10. M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.

Answer: Yes; and.

Q.11. Is it possible to construct a triangle with lengths of its sides as , and ? Give reason for your answer.

Answer: No; Sum of two sides is less than the third side.

Q.12. Is it possible to construct a triangle with lengths of its sides as , and ? Give reason for your answer.

Answer: Yes, because in each case the sum of two sides is greater than the third side.

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