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5) Prove that the bisector of the top angle of an isosceles triangle bisects the base at right angles.

6) Show that in an isosceles triangle, the angles opposite equal sides are equal. (Hint Draw a perpendicular to the un- equal side from the vertex.)

7) In the isosceles triangle ABC AB = AC. Perpendiculars BD and CE are drawn from the vertices B and C, to the opposite sides. Show that BDE = ACE

8) In the square ABCD, show that the two triangles ABC and ADC are congruent to each other.

Question 6)

$Question8)\phantom{\rule{0ex}{0ex}}In\u2206ABCand\u2206ADC\phantom{\rule{0ex}{0ex}}AD=BC---(sidesofasquare)\phantom{\rule{0ex}{0ex}}DC=AB---(sidesofasquare)\phantom{\rule{0ex}{0ex}}AC=AC---(common)\phantom{\rule{0ex}{0ex}}\therefore \u2206ABC\cong \u2206ADC(bySSSproperty)\phantom{\rule{0ex}{0ex}}thusthetwotrianglesarecongruent$

Regards

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