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10., , 11,, , 12,, , , In the adjoining figure,, , Congruence 201, , , , AB = AD and CB = cp,, , ’ oO, Prove that AABC = AADC, ‘ M4, , A Cc, , . B, oO B, Q, , D, , c, , . In the given figure, P4 . AB,, , QB | AB and pa = f, Prove that AOAP = AOBQ, ———e., Is OA = OB?, Ta A, A, , . In the given figure, triangles ABC and DCB are right, angled at A and D respectively and AC = DB,, Prove that AABC = ADCB., s, , B, , In the adjoining figure, AABC is an isosceles triangle in which, , AB =AC. If E and F be the midpoints of AC and AB, , respectively, prove that BE = CF., , Hint. Show that ABCF = ACBE, F, B, , A, E, - ¢, In the adjoining figure, P and Q are two points on equal sides AB A, and AC of an isosceles triangle ABC such that AP = AQ., Prove that BQ = CP. . ., J B ., triangle in which A, i re, AABC is an isosceles, Haak ean aa AC are produced to D and E respectively, such that BD = CE, prove that BE = CD. |, Hint. Show that AACD = AABE., B @ |, 7 E

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200 Mathematics for Class 7, , ngruence a: :, 2. Given below are pairs of congruent triangles. State the property of congr nd nam,, the congruent triangles in each case. Jf R, , AA h, , (iv), , , , 3. In Fig, (i), PL 1 OA and PM | OB such that PL = PM. Is APLO = APMO?, Give reasons in s ipport of your answer,, , A B, (il), , 4. In Fig. (ii), AD = BC and AD || BC. Is AB = DC? Give reasons in support of your answer., Hint. Prove that A ABC = ACDA., , 5. In the adjoining figure, AB = AC and BD = DC., , Prove that AADB = AADC and hence show that, (i) ZADB = ZADC = 90°, (ii) ZBAD = ZCAD., , , , A, , B D C, , 6. In the adjoining figure, ABC is a triangle in which AD is the bisector of, <A.IfAD 1 BC, show that AABC is isosceles,