Q1 In triangles ABC and PQR, ∠A= ∠Q and ∠B = ∠R. Which side of APQR should be equal to side AB of AABC so that the two triangles are congruent? Give reason for your answer.
Q2 In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of APQR should be equal to side BC of AABC so that the two triangles are congruent? Give reason for your answer.
Q3 “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?
Q7 In the given figure, two lines AB and CD intersect each other at the point O such that BC || DA and BC = DA. Show that O is the mid-point of both the line segments AB and CD.
Q9 In the given figure, ∠ABC = ∠ACB, D and E are points on the sides AC and AB respectively such that BE = CD. Prove that (i) ∆EBC ≅ ∆DCB (ii) ∆OEB ≅ ∆ODC (iii) OB = OC.
Q13 (a) In the figure (1) given below, QX, RX are bisectors of angles PQR and PRQ respectively of A PQR. If XS⊥ QR and XT ⊥ PQ, prove that (i) ∆XTQ ≅ ∆XSQ (ii) PX bisects the angle P. (b) In the figure (2) given below, AB || DC and ∠C = ∠D. Prove that (i) AD = BC (ii) AC = BD. (c) In the figure (3) given below, BA || DF and CA II EG and BD = EC . Prove that, . (i) BG = DF (ii) EG = CF.
