Question

7. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB
1 and parallel to BC intersects AC at D. Show that
(1) D is the mid-point of AC
(ii) MD LAC
1
(iii) CM = MA= 1/2AB
​

Answer 1

Answer:

In △ABC,

(1) M is the mid point of AB and

MD∥BC

D is the mid point of AC

(2) As MD∥BC &

AC is transversal

∠MDC+∠BCD=180

∘

∠MDC+90

∘

=180

∘

⇒∠MDC=90

∘

⇒MD⊥AC

(3) In △AMD and △CMD

AD=CD

∠ADM=∠CDM

DM=DM

△AMD≅△CMD

AM=CM⇒AM=

2

1

AB⇒CM=AM=

2

1

AB

Step-by-step explanation:

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