Question

ABC is a triangle right angle at C. A line through the mid - point M of hypotenuse AB and parallel to BC intersects AC at D. Show that :
1:D is mid -point of AC
2:MD is perpendicular to AC
3:CM=MA=1/2 AB
..........plz solve this.I will mark as brainliest

Answer 1

Obviously CM = MA = MB

CM = (1/2)AB

i) 2 triangles AMC and BMD are congruent because MC = MD = MA =MB

and angle AMC = BMD ( opposite )

ii) angle DBC = angle DBA + angle ABC

but angle DBC = angle ACB (alternate conner )

then angle DBC =angle ACB + angle ABC = 90 degrees
(because ABC is a given right triangle)

So angle DBC is a right angle.

iii) Because the 2 right triangles have same BC and AC = BD