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Congruence of triangle
Worksheet on Congruence of triangle is based on congruent triangle. It is based on some axioms like SAS,SSS etc. 1. If Δ ABC is congruent to Δ DEF 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
2. If Δ ABC is congruent to ∆ DEF and ∠ B =∠ E , ∠ C =∠ F , then
(a) AB = DF (b) BC = EF (c) CA = ED (d) ∠ A = ∠ D
3. In Δ ABC and Δ DEF, AB = DF and ∠ A = ∠ D . The two triangles will be congruent by S.A.S axiom if
(a) BC = EF (b) AC = DE (c) BC = DE (d) AC = EF.
4. Δ ABC is congruent to Δ PQR . If AB = 5cm, &ang B = 400 and ∠ A = 800 , then which of the following is true ?
(a) QP = 5 cm , ∠ P = 600 (b) QP = 5 cm, ∠ R = 600 (c) QR = 5cm , ∠ R = 600 (d) QR = 5cm , ∠ Q = 400
5. In the given figure , diagonal AC of a quadrilateral ABCD bisects the angles ∠ A and ∠ C . Prove that AB = AD and CB = CD 6. In the given figure , it is given that BC = CE and ∠ ABG = ∠ DEF. Prove that ∆GCB is congruent to Δ DCE 7. In the given figure , P is a point in the interior of ∠ AOB. If PL is perpendicular to OA and PM is perpendicular to OB such that PL = PM , show that OP is the bisector of ∠ AOB. 8. X and y are two parallel lines intersected by another pair of parallel lines p and q such that line q makes angle 60 with line x . Show that∆ ABC is congruent to Δ CDA. 9. In the given figure , ∠ BAD = 300 , AC = AE , AB = AD. Show that side BC = DE , if ∠ EAC = 300. 10. It is given that Δ ABC is congruent to Δ RPQ . Is it true to say that BC = QR ? Why ?
11. If Δ PQR is congruent to Δ EDF , then is it true to say that PR = EF ? Give reason for your answer.
12. Angles A , B and C of a triangle ABC are equal to each other . Prove that Δ ABC is equilateral.
13. AD , BE and CF , the altitudes of triangle ABC are equal . Prove that ABC is an equilateral triangle.