Question

Extra points!!

Given: Circle M
Given: Segment MA bisects Segment BC
Prove: Angle B is congruent to Angle C

Answer 1

See Explanation

Explanation:

`In \: \odot M, \: \overline{MA} \: bisects \: \overline {BC}\\... (given) \\\\</p><p>\therefore \overline{MN} \: bisects \: \overline {BC}\\... (\because B-N-C) \\\\</p><p>\therefore BN \cong NC... (1)\\\\</p><p>In\: \triangle BMN \:\&\:\triangle CMN\\\\</p><p>BM\cong CM\\ (radii \: of \: same \: circle) \\\\</p><p>MN\cong MN\\ (common \:side) \\\\</p><p>BN \cong NC\\ (from\:1)\\\\</p><p>\triangle BMN \:\cong\:\triangle CMN\\.. (by\: SSS\: postulate) \\\\</p><p>\therefore \angle B\cong \angle C.. (CACT)`