🇹🇭 อ่านบทนี้เป็นภาษาไทย — ความคล้าย (ชั้นมัธยมศึกษาปีที่ 3)
Chapter 8
Similarity and Congruence
Similarity and Congruence
Same shape against same shape and size — and the scale factors for length, area and volume, which are three different numbers and the reason most of these questions are got wrong.
- หลักสูตรแกนกลาง / สสวท.
- การวัดและเรขาคณิต (Geometry and Measure)ตรงกับ ม.3 บทที่ 4 ความคล้าย และ ม.2 บทที่ 8 ความเท่ากันทุกประการ
- Common Core (US)
- 8.G, G-SRT
- Cambridge
- Lower Secondary Stage 9 — Geometry and Measure: geometrical reasoning
8.1 Similar shapes
นิยาม
Similar
Two shapes are similar when every pair of corresponding angles is equal AND every pair of corresponding sides is in the same ratio. Same shape, any size.
| Congruent | Similar | |
|---|---|---|
| angles | equal | equal |
| sides | equal | in a fixed ratio |
| scale factor | any positive number | |
| symbol |
ทำไมถึงเป็นแบบนั้น
Congruence is the special case of similarity where the scale factor is . Every congruent pair is similar; the reverse is not true, and questions about triangles usually turn on knowing which one you have been given.
- Proving two triangles similar
- AA — two pairs of equal angles is enough, since the third follows
- SSS — all three side ratios equal
- SAS — two side ratios equal with the angle between them equal
ข้อควรระวัง
AA proves SIMILARITY but never congruence. Two equilateral triangles of different sizes have identical angles and are not the same shape-and-size — which is exactly the distinction being tested.
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