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Prove that A B C is isosceles if any on...

Prove that ` A B C` is isosceles if any one of the following holds: (i) `A l t i t u d e\ ` AD bisects `B C` (ii) Median `A D` is perpendicular to the base `B C`

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To prove that triangle ABC is isosceles under the given conditions, we will consider each case separately. ### Case 1: Altitude AD bisects BC 1. **Given**: AD is the altitude from vertex A to base BC, and it bisects BC. - This means that BD = DC, where D is the foot of the altitude. 2. **Triangles to Consider**: We will consider triangles ABD and ACD. ...
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RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. A B is a line segment and line l is its perpendicular bisector. If a...

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  2. In quadrilateral A C B D ,\ A C=A D\ a n d\ A B\ bisects /A . Show th...

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  3. Prove that A B C is isosceles if any one of the following holds: (i...

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  4. In Figure, P Q R S is a quadrilateral and T\ a n d\ U are respectively...

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  5. In Figure, P S=Q R\ a n d\ /S P Q=/R Q Pdot Prove that P Q S\ ~=\ Q...

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  6. In right triangle A B C , right angle at C ,\ M is the mid-point of th...

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

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  8. In Figure, the side B A\ a n d\ C A have been produced such that B A...

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  9. In A P Q R , if P Q=P Q\ a n d\ L ,\ M\ a n d\ N are the mid-points o...

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  10. In Figure, PQRS is a square and SRT is an equilateral triangle. Prove ...

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  11. Prove that the medians of an equilateral triangle are equal.

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  12. In a A B C , if /A=120^0a n d\ A B=A Cdot Find /B\ a n d\ /C

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  13. In A B C , if A B=A C\ a n d\ /B=70^0, find /A

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  14. The vertical angle of an isosceles triangle is 100^0dot Find its bas...

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  15. In Figure, AB=AC and /A C D=10^@, find /BAC

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  16. Find the measure of each exterior angle of an equilateral triangle.

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  17. If the base of an isosceles triangle is produced on both sides, prov...

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  18. In Figure, AB=AC and DB=DC , find the ratio /A B D\ :\ /A C D

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  19. Determine the measure of each of the equal angles of a right-angled ...

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  20. A B C is a right-angled triangle is which /A=90^0a n d\ A B=A Cdot F...

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