Geometry for triangle tri the following facts are given: segment an || segment ri at = 8cm ar = 2cm tn = 12cm (a) use a two-column or paragraph format to prove triangle tan ~ triangle tri (b) use the side splitting theorem to find ni.

A)
Statements                                    Reasons
1. Segment AN || Segment RI       1. Given
2. <TAN is congr. to <R                 2. If  2 lines are cut by a tranversal,
                                                        then corresponding angles are congruent
3. <TNA is congr. to <I                  3. Same as 2.
4. Triangle TAN ~ triangle TRI      4. AA

b)
AT/AR = TN/NI

8/2 = 12/NI

4 = 12/NI

4NI = 12

NI = 3

NI = 3 cm