Parallel lines in triangles: TPT-Z, TPT-F and TPT-C (mixed)

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Learn it When a line is parallel to a side of a triangle, the transversals make equal or supplementary angles. TPT-Z: alternate angles are equal (a Z shape). TPT-F: corresponding angles are equal (an F shape). TPT-C: co-interior angles add to 180° (a C shape). Combine these with SATT (the angles of a triangle add to 180°) and SAT (angles on a straight line add to 180°).

Example: DE is drawn through A parallel to BC. ∠DAB = 55° and ∠EAC = 65°. Find ∠BAC.

∠DAB, ∠BAC and ∠EAC lie on the straight line DE, so they add to 180° (SAT).
∠BAC = 180° − 55° − 65° = 60°.
Also ∠ABC = ∠DAB = 55° and ∠ACB = ∠EAC = 65° (TPT-Z), which shows why the angles of any triangle add to 180°.

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