Answer Key — HSG.GPE.B.4

For parents and tutors

Do not share with students before practice tests.

Practice Problems — Sets 1–10

| Set | Guidance | | --- | --- | | Set 1 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 2 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 3 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 4 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 5 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 6 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 7 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 8 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 9 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 10 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. |

Practice Problems — Sets 11–20

| Set | Guidance | | --- | --- | | Set 11 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 12 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 13 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 14 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 15 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 16 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 17 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 18 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 19 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. | | Set 20 | Use coordinates to prove simple geometric theorems algebraically — verify written work and accept reasonable drawings. |

Review tiers 1–10

Checklists are parent-judged.
Written items: verify against practice set patterns.
Standard text: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Practice test scoring

| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |

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