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In right triangle ABC, right-angled at C...

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 `D M\ =\ C M`. Point D is joined to point B (see Fig. 7.23). Show that:
(i) `DeltaA M C~=DeltaB M D`
(ii) `/_DBC` is a right angle
(iii) `Δ DBC ≅ Δ ACB`
(iv) `CM =1/2 AB`

Text Solution

Verified by Experts

`/_ AMC and /_BMD`
AM=BM
MC=MD
`angleAMC=angleBMD`(VOA)
SAS criteria
`/_AMC cong /_BMD`
`angleCAM=angleDBM`
If opposite interiar angles are equal
...
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