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If the bisectors of the base angles of a...

If the bisectors of the base angles of a triangle enclose an angle of `135^0,` prove that the triangle is a right triangle.

Text Solution

Verified by Experts

To prove- `/_ABC` is right angled
`/_OBC=/_B/2`
`/_OCB=/_C/2`
`In /_BOC`
`/_BOC+/_OBC+/_OCB=180^@`
`135^@+/_B/2+/_C/2=180^@`
`1/2(/_B+/_C)=45^@`
`/_B+/_C=90^@`
...
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RD SHARMA-LINES AND ANGLES -All Questions
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  7. In Fig. 6.13, lines AB and CD intersect at O. If /A O C\ +/B O E=70^@...

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  13. Prove that ,The bisectors of base angles of a triangle cannot enclos...

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  14. Name the pairs of adjacent angles in the figures given below :

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  15. In figure, DeltaO D C DeltaO B A ,/B O C=125^oand /C D O=70^o. Find...

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  16. O A\ =\ O Ba n d\ O D\ =\ O C. Show that (i) DeltaA O D~=DeltaB O C a...

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  18. How many pairs of adjacent angles are formed when two lines intersec...

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  19. How many pairs of adjacent angles, in all, can you name in Figure.

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  20. In the figure ,find the value of x.

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