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In quadrilateral A C B D ,\ A C=A D\ a n...

In quadrilateral `A C B D ,\ A C=A D\ a n d\ A B\ ` bisects `/_A` . Show that ` A B C\ ~= A B Ddot` What can you say about `B C\ a n d\ B D ?`

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To solve the problem, we need to show that triangles \( ABC \) and \( ABD \) are congruent, and then determine the relationship between \( BC \) and \( BD \). ### Step-by-Step Solution: 1. **Identify the Given Information:** - In quadrilateral \( ACBD \): - \( AC = AD \) (given) - \( AB \) bisects \( \angle A \) (which means \( \angle CAB = \angle DAB \)) ...
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RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. If D is the mid-point of the hypotenuse A C of a right triangle A B ...

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  2. A B is a line segment and line l is its perpendicular bisector. If a...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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