481. In figure, AD π CD and BC π CD. If AQ = BP and DP = CQ, prove that ∠DAQ = ∠CBP.
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482.In ∆ABC, D is the mid point of BC. The perpendiculars from D to AB and AC are equal. Prove that ∆ABC is isosceles.
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483. In figure, ∆ABD and ∆BCD are isosceles triangles on the same base BD. Prove that ∠ABC = ∠ADC.
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Long Answer Type
484.In ∆’s ABC and PQR, AB = PQ, AC = PR and altitude AM and altitude PN are equal. Show that ∆ABC ≅ ∆PQR.
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485.In figure, the perpendicular AD, BE and CF drawn from the vertices A, B and C respectively of ∆ABC are equal. Prove that the triangle is an equilateral triangle.
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486.ABCD is a parallelogram. If the two diagonals are equal, find the measure of ∠ABC.
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Short Answer Type
487.AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (see figure). Show that the line PQ is the perpendicular bisector of AB.
Short Answer Type
Long Answer Type
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