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In right triangle \( A B C , \) 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 \( D M = C M . \) Point \( D \) is joined to point \( B \) (see Fig. 7.23 ). Show that. (i) \( \Delta \mathrm { AMC } \cong \Delta \mathrm { BMD } \) (ii) \( \angle \mathrm { DBC } \cong \Delta \mathrm { BMD } \) \( \Delta 1 \Delta D B C \cong \Delta A C B \)

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Q1

In right triangle

A B C

, right angled at

C, M

is the mid-point of hypotenuse

A B

.

C

is joined to

M

and produced to a point

D

such that

D M = C M

. Point

D

is joined to point

B

(see figure).
Show that:
(i)

Δ A M C ≅ Δ B M D

(ii)

∠ D B C

is a right angle.
(iii)

Δ D B C ≅ Δ A C B

(iv)

C M = \frac{1}{2} A B

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Q2

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:

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Q3

In right triangle ABC, the right angle is 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 figure).

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Δ A M C ≅ Δ B M D

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Q4

Question 8 (i)
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:

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Q5

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:

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