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7. ABC is a triangle right angled at C. A line through the mid -point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) MD .L AC (iii) CM = MA = 2AB.

7. ABC is a triangle right angled at C. A line through the mid -point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i) D is the mid-point of AC
(ii) MD .L AC
(iii) CM = MA = 2AB.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60782 Points
2 years ago
(i) MD 11 BC, meets AC at D. :. D is mid-point of AC. [A line through the mid-point of a side of a triangle parallel to other D bisects and third side.] C B 122 (f.i) MD II BC and AC is' transversal. ' .. LADM = LACB [Corresponding angles] L ADM = 90° [•: LACB = 90°] MD .L AC. (iii) Consider triangles ADM and CDM, AD = DC MD is common. - ' [From result (i)] LADM =•L. CDM [90° each] [Froin. result (ii)] A ADM ::: A CDM [SAS] ;•. MA.= = 2AB. [•: 14 is mid-point of AB)] (](]

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