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Q1. State the conditions of congruence for the following: (i) line segment (ii) angles, (iii) squares, (iv) rectangles and (v) circles. Q2. Are two triangles congruent if two sides and an angle of one triangle are respectively equal to two sides and an angle of the other? If not under what conditions will be they congruent? Q3. Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles. Q4. In the given figure, and such that . Is ? Give reasons in support of your answer. Q5. In the given figure, Q6. In the given figure, triangles and Prove that © Copyright 2011 - 12 Educomp Solutions Ltd. . Prove that are right angled at . respectively . Page 1 of 6 Q7. In the given figure, are two points on equal sides isosceles triangle Q8. In the given figure, produced to Q9. such that . Prove that of an . is an isosceles triangle in which respectively such that In the following figure, be the mid points of © Copyright 2011 - 12 Educomp Solutions Ltd. . If are , prove that is an isosceles triangle in which respectively, prove that . . If . Page 2 of 6 Q10. In the given figure Q11. If two squares have equal area, are they congruent? If two triangles have equal area they congruent? Q12. Are two figures congruent if their area is equal? Are two circles congruent if they have equal circumference? Q13. In the given figure, such that Q14. bisect each other at . Prove that is an isosceles triangle in which . Prove that bisects . . Also is a point . If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle. Are the two triangles congruent? © Copyright 2011 - 12 Educomp Solutions Ltd. Page 3 of 6 Q15. The sides that Q16. have been produced such that Q18. . Prove . If are equilateral triangles and under which Q17. and are congruent. In the given figure if In the given figure, can you say about © Copyright 2011 - 12 Educomp Solutions Ltd. , state the condition(s) , then find is a rhombus, Are . are congruent? What ? Page 4 of 6 Q19. In the given figure, is the mid point of are equal in length. Prove that Q20. In the given figure and and perpendiculars to sides is an isosceles triangle. . Prove that the triangles are congruent. Answers A1. A2. A3. A4. A5. A6. Hint: (i) same length (ii) same measurement (iii) same side length (iv) same length and breadth (v) Same radius No, Use SAS condition. Hint: Prove that two triangles so formed are congruent. Yes, By RHS condition of congruency. Hint: Use SSS congruence condition. Hint: Use RHS congruence condition. © Copyright 2011 - 12 Educomp Solutions Ltd. Page 5 of 6 A7. Hint: Prove A8. Hint: Show that A9. Show that A10. Hint: Prove that A11. A12. A13. Yes, No NO, Yes Hint: Prove that congruency of triangles A14. A15. A16. A17. No Therefore, angle E = angle C, angle D = angle B. alternate angles are equal then DE is parallel to BC SSS, ASA, SAS Hint: A18. Yes, . By SAS congruence condition, CPCT. are congruent. then conclude. are congruent. By SSS condition of congruency. Also, A19. . are congruent. By SSS condition of congruency. Hint: by CPCT. A20. Property of Isosceles triangle. Hint: Use ASA congruence condition. © Copyright 2011 - 12 Educomp Solutions Ltd. Page 6 of 6