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If D is any point on the base B C pro...

If `D` is any point on the base `B C` produced, of an isosceles triangle `A B C ,` prove that `A D > A B` .

Text Solution

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In `/_\ABC`, we have:
`AB=AC`
`=>/_ABC=/_ACB` .....(i) [ since, Angle opp. to equal sides are equal]
In `/_\ABD`, we have:
`/_ABC>/_ADB`
`=>/_ABC>/_ADB` ......(ii)
From (i) and (ii), we get:
`/_ACB>/_ADB`
`=>/_ACD>/_ADC` [since, `/_ACB=/_ACD`, `/_ADB=/_ADC`]
`=>AD>AC` [since, Side opposite to greater angle is larger]
`=>AD > AB` [since, `AB=AC`]
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RD SHARMA-CONGRUENT TRIANGLE -All Questions
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  2. In Figure, A B > A Cdot Show that A B > A D

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  3. If D is any point on the base B C produced, of an isosceles tria...

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  4. In Figure, if A D is the bisector of L A , show that: A B > B D (ii) ...

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  5. Show that in a right angled triangle, the hypotenuse is the longest...

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  6. In Figure, A C > A B and A D is the bisector of L A . Show that A D C ...

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  7. Show that the sum of the three altitudes of a triangle is less than...

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  8. Prove that any two sides of a triangle are together greater than twi...

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  9. Prove that the perimeter of a triangle is greater than the sum of it...

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  10. Show that the difference of any two sides of a triangle is less than...

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  11. In Figure, P Q R is a triangle and S is any point in its interior, s...

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  12. In P Q R , S is any point on the side Q R . Show that P Q+Q R+R P >...

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  13. In Figure, A P\ |l\ a n d\ P R > P Q . Show that A R > A Q Given: A P...

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  14. In Figure, P Q R S is a quadrilateral. P Q is its longest side and R...

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  15. In Figure, P Q R S is a quadrilateral in which diagonals P R\ a n d\...

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  16. Of all the lines segments drawn from a point P to a line m not conta...

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  17. In Figure, /E >/A\ a n d\ /C >/D . Prove that A D > E C

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  18. In Figure, T is a point on side Q R of P Q R and S is a point such th...

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  19. In Figure, A C > A B\ a n d\ D is the point on A C such that A B=A Ddo...

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  20. In Figure, A B\ a n d\ C D are respectively the smallest and longest...

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