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In an isosceles triangle altitude from t...

In an isosceles triangle altitude from the vertex bisects the base. GIVEN : An isosceles triangle `A B C` such that `A B=A C` and an altitude `A D` from `A` on side `B Cdot` TO PROVE : `D` bisects `B C` i.e. `B D=D Cdot` Figure

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Given- `AB=AC`
TO prove= BD=CD
Proof-`In /_ADB and /_ACD`
`/_ADB=/_ADC`(each 90)
`AD=AD`(common)
`/_B=/_C`
`/_ADB cong /_ACD`(AAS)
BD=CD.
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RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. In Figure, A C=B C ,/D C A=/E C B and /D B C=/E A Cdot Prove that tria...

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  2. If the bisector of the vertical angle of a triangle bisects the base...

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  3. In an isosceles triangle altitude from the vertex bisects the base....

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  4. If the altitude from one vertex of a triangle bisects the opposite ...

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  5. Angles opposite to two equal sides of a triangle are equal. GIVEN : ...

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

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  7. In A B C , side A B is produced to D so that B D=b cdot If /B=60^0 an...

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  8. Prove that in a quadrilateral the sum of all the sides is greater t...

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  9. In Figure, P Q R S is a quadrilateral in which diagonals P R and Q S i...

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  10. GIVEN : P Q R S is a quadrilateral. P Q is its longest side and R S ...

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  11. In Figure, A B and CD are respectively the smalles and longest sides...

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  12. Of all the line segments drawn from a point P to a line m not containi...

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  13. In Figure, A D is a median and B L ,C M are perpendiculars drawn from ...

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  14. In Figure, B M and D N are both perpendiculars to the segments A C and...

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  15. If A B C is an isosceles triangle with A B=A C . Prove that the ...

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  16. If the altitudes from two vertices of a triangle to the opposite sid...

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  17. A D and B C are equal perpendiculars to a line segment A B . Show that...

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  18. In A B C ,A B=A C , and the bisectors of angles B and C intersec...

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  19. In Figure, it is given that A B=E F ,B C=D E ,A B|B D and F E|C Edot P...

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  20. In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C ...

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