Question

Geometry Help!!

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.

Answer 1

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