Question

PLEASE HELP! Complete each congruency statement and name the rule that is used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write "CNBD" for "Cannot be determined" in place of the rule. M is the midpoint of line CI. ΔCAM ≅ Δ____ by ____

Answer 1

It's CNBD. Leave the first blank...well blank

Answer 2

In the situation where segment
`\overline {AM}` is perpendicular to segment
`\overline {CI}`, such that
`\overline {AM}` is the perpendicular bisector to segment
`\overline {CI}` we have the following two column proof;

Statement
`{}` Reason

M is the midpoint of
`\overline {CI}`
`{}` Given

`\overline {CM}` ≅
`\overline {IM}`
`{}` Definition of midpoint

`\overline {AM}` ≅
`\overline {AM}`
`{}` Reflexive property

∠CMA = ∠IMA = 90°
`{}` Definition of perpendicular bisector

ΔCAM ≅ ΔIAM
`{}` By the Side-Angle-Side (SAS) rule of congruency

However, where the segment
`\overline {AM}` is not be assumed as perpendicular to segment
`\overline {CI}`, then CNBD

Explanation: