Class 7 Science

Chapter 7 Congruence of Triangles

Important Questions Set 3

 

Q.1. Show that the given triangles are congruent.

Q.2. In the figure, ∆ABC is an isosceles triangle in which AB =AC and AD is a median. Prove that:

(i) ∆ADB ≅ ∆ADC

(ii) ∠BAD = ∠CAD

Q.3. AB is a line segment, AX and BY are two equal line segments drawn on opposite sides of line AB such that AX || BY. If AB and XY intersect each other at P, prove that ∆APX = ∆BPY.

Q.4. In the given figure, we have C is the midpoint of AB and DA = DB. Prove that : ∠DCA = ∠DCB.

Q.5. In the figure, ∆ABC is an isosceles triangle in which AB = AC and AD is the bisector of ∠A. Prove that:

(i) ∆ADB ≅ ∆ADC

(ii) ∠B= ∠C

(iii) BD = CD

(iv) AD ^ BC

Q.6. In the given figure, we have PQ = SR and PR = SQ. Prove that:

(i) ∆PQR ≅ ∆SRQ

(ii) ∠PQR = ∠SRQ

Q.7. Prove that the diagonals of a parallelogram bisect each other.

Q.8. In the given figure, ∆ABC is an isosceles triangle in which AB = AC. If BM ^ AC and CN ^ AB, prove that:

(i) ∆BMC ≅ ∆CNB

(ii) BM = CN

Q.9. In the figure, it is given that LM = NM, ML ^ PQ and MN ^ PR. Prove that ∠LPM = ∠NPM.

Q.10. Show that the diagonals of a rhombus bisect each other at right angles.

Q.11. If the opposite sides of a quadrilateral are equal, prove that the quadrilateral is a parallelogram.

Q.12. In both the given figures, AB = AC and DB = DC.

Prove that ∠ABD = ∠ACD.

Q.13. In the given figure, triangles ABC and DCB are right angled at A and D respectively and AC = DB, then prove that
∠ACB = ∠DBC.

Q.14. In the given figure, AB = AC and AD = AE.

Prove that:

(i) ∆ABD ≅ ∆ACE

(ii) BE = CD

Q.15. If the two diagonals of a quadrilateral bisect each other, prove that the quadrilateral will be a parallelogram.

Q.16. In the given figure, if PS is the angle bisector of ∠QPR then, show that ∆PQS ≅ ∆PRS

Q.17. In the given figure, KK' and LL' are equal and perpendicular to AC. Show that ∆KK'M and ∆LL'M are congruent.

 

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