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

1.	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) ΔAMC≅ΔBMD(ii) ∠DBC is a right angle.(iii) ΔDBC≅ΔACB(iv) CM=12AB
Answer» 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 the given 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) $C M = \frac{1}{2} A B$

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) ΔAMC≅ΔBMD(ii) ∠DBC is a right angle.(iii) ΔDBC≅ΔACB(iv) CM=12AB

Answer»

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 the given 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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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) ΔAMC≅ΔBMD(ii) ∠DBC is a right angle.(iii) ΔDBC≅ΔACB(iv) CM=12AB

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