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RHS Rule

In right tria...

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:
$Δ A M C ≅ Δ B M D$

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Solution

$(i) I n Δ A M C a n d Δ B M D, A M = B M (M i s t h e m i d p o i n t o f A B) ∠ A M C = ∠ B M D (v e r t i c a l l y o p p o s i t e a n g l e s) C M = D M (G i v e n) ∴ Δ A M C ≅ Δ B M D (b y S A S c o n g r u e n c e r u l e)$

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Q. 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:

Δ A M C ≅ Δ B M D

Q. 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:

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

Q. 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:

∠ D B C i s a r i g h t a n g l e .

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).

State whether the statement is true/false

Δ A M C ≅ Δ B M D

Q. Question 8 (iv)
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:

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

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