Study Guide — HSG.SRT.D.9
(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle b…
Establish similarity with dilations and use proportions in triangles.
What this standard means
- (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
- Apply (+) derive the formula a = 1/2 ab sin(c) for the area of a triangle b… with models and explanation
- Proves or identifies similarity
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Set up proportions from similar triangles 2. Use trig ratios in right triangles 3. Scale lengths by the similarity ratio
_See printable PDF for diagram._
Common mistakes
- Mismatching corresponding sides
- Trig ratio on wrong angle
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSG.SRT.D.9.
- [ ] Proves or identifies similarity
- [ ] Solves proportions from similar figures
- [ ] Applies trig ratios correctly
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors