Question

(5
Section C (Long Answer Type Questions)
X 3 = 15)
11. The taxi fare in a city is as follows: For the first kilometer the fare is Rs 8 and for
the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and
total fare as Rs y, write a linear equation for this information, and draw its graph.
OR
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 Fig.
7.23). Show that:
() A AMC A BMD (ii) ZDBC is a right angle. (iii) A DBC = A ACB (iv) CM =
AB.​

Answer 1

Answer:

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

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