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Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.
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Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.

Write the complete proof in your paper homework and for online (only) complete the-example-1
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Explanation:


m\angle ADB = m\angle CDB... (given) \\\\</p><p>\therefore m\angle ADM = m\angle CDM... (1)\\</p><p>(\because D-M-B) \\\\</p><p>In\: \triangle 's ADM \: \&amp;\: CDM\\\\</p><p>\overline{AD} \cong\overline {CD} ... (given) \\\\</p><p>m\angle ADM = m\angle CDM.(From \:1)\\\\</p><p>\overline{DM} \cong\overline{DM} ... (given) \\\\</p><p>\therefore \triangle ADM \: \cong\: \triangle CDM\\.. (By \: SAS\: postulate) \\\\</p><p>\therefore \overline{AM} \cong\overline{CM}..(2)\\(by\: c. s. c. t.) \\\\</p><p>m\angle AMD = m\angle CMD..(3)\\(by\: c. a. c. t.)\\\\</p><p>\because m\angle AMD + m\angle CMD= 180\degree ..(4)\\</p><p>(Linear\: pair\: \angle 's)\\\\</p><p>\therefore m\angle AMD + m\angle AMD= 180\degree \\..(From \: 3 \: \&amp; \: 4)\\\\</p><p>\therefore 2m\angle AMD = 180\degree\\\\</p><p></p><p>\therefore m\angle AMD = (180\degree)/(2)\\\\</p><p>\therefore m\angle AMD =90\degree \\\\</p><p>\red{\implies \overline{MD} \perp\overline{AM}} \\\\</p><p>\implies m\angle AMB=m\angle CMB= m\angle CMD = 90\degree.. (5)\\\\</p><p></p><p>In\: \triangle 's ABM \: \&amp;\: CBM\\\\</p><p>\overline{AM} \cong\overline{CM}\\.(From \: 2)\\\\</p><p>m\angle AMB=m\angle CMB\\..(each\: 90\degree) \\\\</p><p>\overline{BM} \cong\overline{BM} ... (common) \\\\</p><p>\therefore \triangle ABM \: \cong\: \triangle CBM\\.. (By \: SAS\: postulate) \\\\</p><p>\therefore m\angle BAM = m\angle BCM\\(by\: cact) \\\\</p><p>\purple {\implies m\angle BAC = m\angle BCA} \\(\because A-M-C)

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