Question

In right triangle ABC, right angled at C, M is the mid-point of

hypotenuse AB. C is joined to M and produced to a point D

such that DM = CM. Point D is joined to point B (see the given figure).Show that:

(i) 

AMC =BMD

(ii) 

<DBC is a right angle.

(iii) 

DBC =ABC


(iv) CM =1/2 AB

​

Answer 1

i) △AMC≅△BMD

Proof: As 'M' is the midpoint

BM=AM

And also it is the mid point of DC then 

DM=MC

And AC=DB (same length)

∴Therefore we can say that

∴△AMC≅△BMD

ii) ∠DBC is a right angle

As △DBC is a right angle triangle and

DC2=DB2+BC2 (Pythagoras)

So, ∠B=90°

∴∠DBC is 90°

iii) △DBC≅△ACB

As M is the midpoint of AB and DC. So, DM=MC and AB=BM

∴DC=AB (As they are in same length)

And also, AC=DB

and ∠B=∠C=90°

By SAS Axiom

∴△DBC≅△ACB

iv) CM=21AB

As △DBC≅△ACB

CM=2DC

∴DC=AB(△DBC≅△ACB)

So, CM=2AB

∴CM=21AB

Answer 2

Answer:

• we are told to hate our brothers (i.e. people belonging to other countries) at the time of war. Political leaders and powerful people, who work for their personal gains, ask us to do so. However, we should not act as a puppet in their hands and do as they say. We should under stand that war is futile and analyse the situation before jumping to conclusions. The poet asks us to remember that by hating our brothers, we are dispossessing, betraying and condemning ourselves. When we take arms against each other, we pollute the human earth and violate the purity of the atmosphere.