Question

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 ______

Answer 1

Answer:

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

Step-by-step explanation:

Given that ΔABC is an isosceles triangle, with $\overline{BA}$ ≅ $\overline{BC}$

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

∠ABM = ∠CBM

Also we have;

$\overline{BD}$ ≅ $\overline{BD}$  - Reflexive property

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

Therefore;

$\overline{AD}$ ≅ $\overline{CD}$ Corresponding sides of congruent triangles are congruent CPCTC

$\overline{AM}$ ≅ $\overline{CM}$ - AC is bisected by $\overline{BM}$ where  $\overline{BM}$ = Median line

$\overline{DM}$ ≅ $\overline{DM}$  - Reflexive property

Therefore, we have;

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