Advertisement Remove all ads

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 - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

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 ⊥ AC

(iii) CM = MA = 1/2AB

Advertisement Remove all ads


(i) In ΔABC,

It is given that M is the mid-point of AB and MD || BC.

Therefore, D is the mid-point of AC. (Converse of mid-point theorem)


(ii) As DM || CB and AC is a transversal line for them, therefore,

∠MDC + ∠DCB = 180º (Co-interior angles)

∠MDC + 90º = 180º

∠MDC = 90º

∴ MD ⊥ AC


(iii) Join MC.


AD = CD (D is the mid-point of side AC)

∠ADM = ∠CDM (Each 90º)

DM = DM (Common)

∴ ΔAMD ≅ ΔCMD (By SAS congruence rule)

Therefore, AM = CM (By CPCT)

However, AM = 1/2AB (M is the mid-point of AB)

Therefore, it can be said that

CM = AM = 1/2AB

Concept: The Mid-point Theorem
  Is there an error in this question or solution?


NCERT Class 9 Maths
Chapter 8 Quadrilaterals
Exercise 8.2 | Q 7 | Page 151

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads

View all notifications

      Forgot password?
View in app×