Question

Q) in the given figure
m is the mid point of ab
dm || cb
angle d - 90

prove - (i) D is the midpoint of ac
(ii) MD _ |_ AC
(iii)CM = MA = 1/2AB

Answer 1

Answer:

your proof is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: prove : \\ 1.D \: is \: midpoint \: of \: AC \\ 2.MD \: ⊥ \: AC \\ 3.CM=MA= \frac{1}{2} AB \\ \\ proof : \\ since \: M \: is \: midpoint \: of \: AB \\ AM=MB = \frac{1}{2}AB \\ \\ moreover \: as \: DM \: || \: BC \\ by \: thales \: intercept \: theorem \\ \frac{AD}{DC} = \frac{AM}{MB} \\ \\ = \frac{AM}{AM} \\ \\ AD = DC \\ ie \: we \: conclude \: that \: \\ D \: is \: midpoint \: of \: AC$

$here \: ∠ACB = 90 \\ and \: as \: CB \: || \: DM \\ by \: corresponding \: angles \: axiom \\ ∠ACB = ∠ADM = 90 \\ ie \: MD \: ⊥ \: AC$

$similarly \: proving \: CM = AM \\ by \: geometric \: mean \: theorem \\ we \: can \: say \:t hat \\ \\ CM = AM = \frac{1}{2} AB$