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For the following facts are given:
Segment AN Segment RI
AT = 8 cm
AR = 2 cm
TN = 12 cm

(a) Use a two-column or paragraph format to prove
(b) Use the Side-Splitting Theorem to find NI.

Answer :

(a) Since the segments AN and RI are parallel, the corresponding angles TAN and TRI are equal, and the corresponding angles TNA and TIR are equal. Angle ATN is obviously equal to angle RTI. With three matching angles, triangle TAN ~ triangle TRI 

(b) Since AN is parallel to RI, the ratio AR/AT is equal to NI/TN. Thus, 2/8 = NI/12, NI = 3 cm

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