Angles, Parallel Lines and Polygons

The angle facts that come with a pair of parallel lines, the interior and exterior angles of any polygon, and how to write a reason rather than just an answer.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ตรงกับ ม.2 บทที่ 9 เส้นขนาน และบทที่ 10 การให้เหตุผลทางเรขาคณิต
Common Core (US): 8.G, G-CO
Cambridge: Lower Secondary Stage 8 — Geometry and Measure: geometrical reasoning

7.1 Angles made by a transversal

Name	Where they are	Relationship	Shape to look for
corresponding	same position at each crossing	equal	letter F
alternate	opposite sides, between the lines	equal	letter Z
co-interior	same side, between the lines	add to $18 0^{\circ}$	letter C

The three facts — true ONLY when the lines are parallel

ข้อควรระวัง

All three need the lines to be parallel, and a diagram that merely looks parallel is not enough — the question must say so, or the arrows must be marked on the lines.

เคล็ดลับ

Only the C-shape pair ADDS to $18 0^{\circ}$ ; the F and Z pairs are equal. Students who remember "parallel lines make angles equal" and stop there get co-interior questions wrong every time.

ตัวอย่าง

Two parallel lines are crossed by a transversal, making an angle of $6 5^{\circ}$ . Find the alternate angle and the co-interior angle.

วิธีทำ

1.Alternate angles are equal
2.Co-interior angles add to $18 0^{\circ}$ : $180 - 65$

ตอบ Alternate $= 6 5^{\circ}$ ; co-interior $= 11 5^{\circ}$

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