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WS7 – TRIANGLES 1) Show that in a right angled triangle, the hypotenuse is the longest side. 2) BE and CF are two equal altitudes of ∆ABC. Prove that the ∆ABC is isosceles. 3) In ∆ABC, AD is the perpendicular bisector of BC. Show that ∆ABC is an isosceles triangle in which AB = AC. 4) In the figure, AC = AE, AB = AD and BAD = EAC. Show that BC = DE. 5) In the adjoining figure, PR > PQ and PS bisects QPR. Prove that PSR >PSQ. 6) Two sides AB , BC and median AM of one triangle ABC are respectively equal to sides PQ , QR and median PN of PQR . Show that ABC PQR 7) In the following figure AB is a line segment and P is its midpoint. D and E are points on the same side of AB such that BAD ABE and EPA DPB . Show that i) DAP EBP ii) AD = BE 8) In the given figure it is given that AF = AE and BE = CF. Prove that ABC is isosceles. 9) Prove that the angles opposite to equal sides of an isosceles triangle are equal. 10) AD and BC are equal perpendiculars to a line segment AB (see Fig.). Show that CD bisects AB. 11) The land for temple is in the form of an isosceles triangle ABC is in which AB = AC. In order to make additional facilities and make the shape still proper, a donor donated the adjacent land in such a way tha the side BA is produced to D such that AD = AB (see Fig.). Show that BCD is a right angle. What is the value learnt in this act? 12) ABC and DBC are two isosceles triangles on the same base BC. Show that ABD = ACD. 13) In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see the figure). Show that AD = AE. 14) In the figure, sides AB and AC of ABC are extended to points P and Q respectively. Also, PBC < QCB. Show that AC > AB. 15) “Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle” – Prove.