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In right triangle ABC? C is a right angle .M is mid point of hypotenuse AB.C is joined to M and produced to a point D such that DM=CM .then D is joined to B.proved that |
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Answer» △AMC≅△BMDProof: As 'M' is the midpointBM=AMAnd also it is the mid point of DC then DM=MCAnd AC=DB (same length)∴Therefore we can say that∴△AMC≅△BMDii) ∠DBC is a right angleAs △DBC is a right angle TRIANGLE andDC 2 =DB 2 +BC 2 (Pythagoras)So, ∠B=90°∴∠DBC is 90°iii) △DBC≅△ACBAs 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=DBand ∠B=∠C=90°By SAS Axiom∴△DBC≅△ACBiv) CM= 21 ABAS △DBC≅△ACBCM= 2DC ∴DC=AB(△DBC≅△ACB)So, CM= 2AB ∴CM= 21 ABStep-by-step EXPLANATION:mark me the BRAINIEST thank me SUPPORT me |
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