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In two right triangles, one side and a...

In two right triangles, one side and an acute angle of one triangle are equal to one side and the corresponding acute angle of the other triangle. Prove that the two triangles are congruent.

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Let `ABC and DEF` be two right triangles
`/_A=/_D,BC=EF and /_B=/_E=90^@`
Thus, in `/_\s ABC and DEF, we have/_A=/_D,/_B=/_E=90^@`
`BC=EF`
So, by AAS congruence criterion, we obtain `/_\ABC~=/_\DEF`
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RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. In Figure, if A B||D C\ a n d\ P is the mid-point B D , prove that P i...

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  2. In Figure, /B C D=/A D C\ a n d\ /A C B=/B D Adot Prove that A D=B C\ ...

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  3. In two right triangles, one side and an acute angle of one triangle ...

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  4. In Figure, A C=B C ,\ /D C A=/E C B\ a n d\ /D B C=E A Cdot Prove that...

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  5. In Figure, it is given that R T=T S ,\ /1=2/2\ a n d\ /4=2/3 . Prove...

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  6. Two lines A B\ a n d\ C D intersect at O such that B C is equal and pa...

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  7. B D\ a n d\ C E are bisectors of /B\ a n d\ /C of an isosceles A B C ...

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  8. In Figure, A B=A C\ a n d\ D B=D Cdot\ Prove that /A B D=/A C D

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  9. \ a b c is an isosceles triangle with A B=A Cdot Side B Ais produced...

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  10. In Figure, A B=A CdotB E\ a n d\ C F are respectively the bisectors ...

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

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

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  13. In Figure, it is given that /A=/C\ a n d\ A B=B Cdot Prove that A B...

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  14. A D\ a n d\ B C are equal perpendiculars to a line segment A B . Sho...

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  15. In A B C ,\ A B=A C , and the bisectors of angles B\ a n d\ C inter...

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  16. In Figure, it is given that A B=E F ,\ B C=D E ,\ A B\ |B D\ a n d\ ...

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  17. In Figure, it is given that A B=B C\ a n d\ A D=E Cdot Prove that a...

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  18. In Figure, l||m and M is the mid-point of the line segment A B . Pro...

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  19. In Figure, line l is the bisector of angle A\ a n d\ B is any point ...

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  20. In Figure, A D is a median and B L ,\ C M are perpendiculars drawn f...

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