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Chapter 7 : Triangles
Q. ABCD is a quadrilateral in which AD=BC and DAB=CBA . Prove that
(i) ABDBAC
(ii) BD=AC
(iii) ABD=BAC
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Q. Prove that the angles of an equilateral triangle are 60 each.
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Q.

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Show that ΔABEΔACF
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Q. In given figure AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
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Q. l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that ABCCDA
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Q. In given figures two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of PQR. Show that:
(i) ABMPQN
(ii) ABCPQR
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Q.

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig.). Show that
(i) ABEACF
(ii) AB=AC, i.e., ABC is an isosceles triangle.
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Q. AD is an altitude of an isosceles triangle ABC in which AB=AC. Show that
(i) AD bisects BC (ii) AD bisects A
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Q. ABC is a right angled triangle in which A=90 and AB=AC. Find B and C.
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Q. ABC and DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that
(i) ABDACD
(ii) ABPACP
(iii) AP bisects A as well as D.
(iv) AP is the perpendicular bisector of BC.
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Q. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that BAD=ABE and EPA=DPB. Show that
(i) DAPEBP
(ii) AD=DE
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Q. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
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Q. In right angled triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM=CM. Point D is joined to point B. Show that:
(i) AMCBMD
(ii) DBC is a right angle.
(iii) DBCACB
(iv) CM=12AB
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Q. ABC is an isosceles triangle in which AB=AC. Sides BA is produced to D such that AD=AB. Show that BCD is a right angle.
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Q. In given figure ABC and DBC are two isosceles triangles on the same base BC. Show that ABD=ACD.
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Q. In Fig, AC=AE, AB=AD and BAD=EAC. Show that BC=DE
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Q. Line l is the bisector of an angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of A. Show that:
(i) ABPAQB
(ii) BP=BQ or B is equidistant from the arms of A.
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Q. In an isosceles triangle ABC, with AB=AC, the bisectors of B and C intersect each other at O. Join A to O. Show that :
(i) OB=OC (ii) AO bisects A
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Q.

In quadrilateral ACBD, AC=AD and AB bisects A. Show that ABCABD. What can you say about BC and BD?
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Q. In ABC, AD is the perpendicular bisector of BC. Show that ABC is an isosceles triangle in which AB=AC.
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