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Q.


In right triangle ABC  , right angled at C  , M   is the midpoint of hypotenuse AB. C is joined to M and produced to a point D such that DM=CM  . Point D is joined to point B. Is it true that Question Image?

Question Image

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a

True

b

False 

answer is A.

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Detailed Solution

Given that,
ABC  is a right-angle triangle, which is right angled at C.
M is midpoint of hypotenuse AB,
So, AM=BM.
And given, Question Image.
 Question ImageSAS Congruence rule:
If an angle and any two sides of one triangle are equivalent to the corresponding two sides and the angle of the second triangle, then the two triangles are said to be congruent.
When two lines intersect each other and form opposite angles due to their intersection, then that angle is said to be a vertically opposite angle.
We know that, Question ImageSo, AC=BD   ……. (1)
Consider, Question ImageQuestion ImageBy SAS congruence criteria,
Question ImageTherefore, it is true that Question ImageHence, option 1 is correct.
 
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