10th Grade · Week 1 of 36 · Math
Geometry undefined terms; segments, rays; distance
1. Hook
- Read (or listen to) what you’re learning. Don’t jump to the quiz.
- Walk the worked example. Then use the interactive lab on this page.
- Guided set → independent set → mastery check → teach-back.
- If you write a paper, stay on campus: Citation Helper, Source Library, Paper Studio.
This is self-paced homeschool on Life Academy. Everything you need is on this page.
You can't define "point" using simpler words. Geometry starts with a few undefined terms. What can you build from them?
Then: lab → guided → quiz → teach it back. The lab is the lesson, not a decoration.
2. Teach
Use undefined terms (point, line, plane) to define segments and rays, and find distance on a number line and in the coordinate plane.
Standards alignment: CCSS.MATH.CONTENT.HSG (domain-level; works with any state’s standards)
STEM this week is Geometry undefined terms; segments, rays; distance: units, a model, and a check another student could repeat.
- Undefined terms: point, line, plane; defined terms include segment (two endpoints) and ray (one endpoint, extends forever).
- Distance on a number line: |b − a|.
- Distance formula: d = √((x₂ − x₁)² + (y₂ − y₁)²).
Segment AB has endpoints A and B; ray AB starts at A and passes through B forever. Points on −3 and 5 are |5 − (−3)| = 8 apart.
Distance from (1, 2) to (4, 6): √(3² + 4²) = √25 = 5. The distance formula is the Pythagorean theorem on the coordinate grid.
- Find the distance from (−2, 3) to (4, −5).
- Δx = 6, Δy = −8.
- d = √(36 + 64) = √100.
- d = 10.
Find the distance between (−1, −1) and (5, 7), and explain the difference between ray PQ and ray QP.
Subtracting coordinates in mixed order, or forgetting to square before adding.
GPS, maps, and game engines compute distances with this same formula.
No classroom teacher today — this page is the lesson. Follow the how-to, then the lab, then the quiz. Follow Lesson Studio, then the lab, then the quiz. Open Transcripts for credits and grades.
Interactive lab (on this page)
Change one variable. Record what happened. This model is the lab — not an off-site sim.
Your work — type it here
Type the answer. Then tap Check my work. This is the assignment — not optional reading.
3. Guided practice
Try these with me — type the missing word, then check.
Reveal the thinking
Find the horizontal and vertical changes, square them, add, and take the square root.
4. Independent practice
Work the set. Check when finished — this is practice (mastery quiz is next).
5. Mastery check
Scored quiz — results save to your gradebook.
Show the math — don't only tap a letter
The lab is the worked example you can move. Then the quiz checks that you own Geometry undefined terms; segments, rays; distance.
Research Desk · Transcripts · Gradebook
Honest limit: We did not film a custom movie for every core lesson. The teach-back, the on-page lab, and the campus library are the curriculum. The teach-back, the on-page lab, and Lesson Studio are the lesson.
6. Reflection / teach-back
Teach-back: Explain Geometry undefined terms; segments, rays; distance in your own words. Give one example and name the usual mistake.