Use a Stated If-Then Rule
An implication allows its conclusion when its hypothesis holds.
About 20 minutes, plus any extended practice
Open lesson 1Geometry: Claims, Converses, and Proof
Geometry arguments connect definitions, givens and established properties. A conclusion needs a chain of reasons; an attractive diagram may suggest a relation but does not establish every length, angle or universal claim.
Before you begin
- Recognize squares, rectangles and triangles; distinguish a statement from its supporting reason.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Reverse a Statement without Assuming Its Truth
A converse swaps an implication’s hypothesis and conclusion.
About 20 minutes, plus any extended practice
Open lesson 2Refute a Universal Geometric Claim
A universal claim fails if one permitted example satisfies its hypothesis but violates its conclusion.
About 20 minutes, plus any extended practice
Open lesson 3Use Transitivity to Connect Equal Segments
If a first segment equals a second and that second equals a third, transitivity establishes equality of the first and third.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Geometry: Claims, Converses, and Proof
These references informed the topic selection. They do not certify complete standards alignment.