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Solve the problems. 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. In isosceles triangle ∆ABC, BM is the median to the base AC . Point D is on BM . Prove the following triangle congruencies: b ∆AMD ≅ ∆CMD △ AM D≅△CMD by rule ______

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Answer:

ΔAMD ≅ ΔCMD by Side Side Side (SSS) congruency rule

Step-by-step explanation:

Given that ΔABC is an isosceles triangle, with [tex]\overline{BA}[/tex] ≅ [tex]\overline{BC}[/tex]

With BM as the median line from B to AC, we have;

∠ABM = ∠CBM

Also we have;

[tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex]  - Reflexive property

Therefore, ΔABD ≅ ΔCBD Side Angle Side SAS condition of congruency

Therefore;

[tex]\overline{AD}[/tex] ≅ [tex]\overline{CD}[/tex] Corresponding sides of congruent triangles are congruent CPCTC

[tex]\overline{AM}[/tex] ≅ [tex]\overline{CM}[/tex] - AC is bisected by [tex]\overline{BM}[/tex] where  [tex]\overline{BM}[/tex] = Median line

[tex]\overline{DM}[/tex] ≅ [tex]\overline{DM}[/tex]  - Reflexive property

Therefore, we have;

ΔAMD ≅ ΔCMD - Side Side Side (SSS) congruency rule

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