# Worksheet Congruence of triangle

Congruence of triangleWorksheet 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 = 60

^{0}(b) QP = 5 cm, ∠ R = 60

^{0}

(c) QR = 5cm , ∠ R = 60

^{0}(d) QR = 5cm , ∠ Q = 40

^{0}

**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 = 30**

^{0}, AC = AE , AB = AD. Show that side BC = DE , if ∠ EAC = 30^{0}.**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.**

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