Question

in the right triangle ABC right angle is at C M is the midpoint 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
show that CM=1/2AB​

Answer 1

Answer:

Step-by-step explanation:

△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

DC

2

=DB

2

+BC

2

(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=

2

1

​

AB

As △DBC≅△ACB

CM=

2

DC

​

∴DC=AB(△DBC≅△ACB)

So, CM=

2

AB

​

∴CM=

2

1

​

AB