Geometry · Elite Guided Teaching Studio
Discover → Manipulate → Classify → Solve → Prove → Transfer. Eighteen missions, one mathematical journey.
Learning map — prerequisite dependencies
Missions unlock as you visit their prerequisites. Progress conceptually, not in isolation.
Prerequisite Readiness
I can recall angles, supplementary pairs, and basic line notation so I am ready to study transversals.
Lines, Rays, Angles & Notation
I can name lines, rays, segments, and angles using correct mathematical notation.
Requires: M0
Complementary, Supplementary & Linear Pairs
I can identify linear pairs and explain why they are supplementary, independent of parallel lines.
Requires: M1
Vertical Angles
I can identify vertical angles and prove they are congruent without any parallel-line assumption.
Requires: M2
What Is a Transversal?
I can identify a transversal and name the eight angle regions it creates across two lines.
Requires: M3
Corresponding Angles
I can identify corresponding angles and state that they are congruent when lines are parallel.
Requires: M4
Alternate Interior Angles
I can identify alternate interior angles and state that they are congruent when lines are parallel.
Requires: M5
Alternate Exterior Angles
I can identify alternate exterior angles and state that they are congruent when lines are parallel.
Requires: M6
Same-Side Interior Angles
I can identify same-side interior angles and state that they are supplementary when lines are parallel.
Same-Side Exterior Angles
I can identify same-side exterior angles and state that they are supplementary when lines are parallel.
Requires: M8
One Angle Unlocks All Eight
I can determine all eight angle measures from a single known angle using a valid theorem chain.
Requires: M5, M6, M7, M8, M9, M3
Algebra + Angle Relationships
I can classify the relationship, name the theorem, then set up and solve the algebraic equation.
Requires: M10
Converse Theorems & Proving Parallel Lines
I can distinguish forward theorems from their converses and use a converse to prove lines are parallel.
Requires: M11
Mixed Classification Laboratory
I can classify any angle pair across all relationship types without hints under mixed conditions.
Requires: M12
Error Detective Laboratory
I can locate the first incorrect step in flawed reasoning, name the violated principle, and correct it.
Requires: M13
Proof & Mathematical Explanation Laboratory
I can write a short structured proof using given, relationship, theorem, and conclusion.
Requires: M12, M14
Triangle Similarity Bridge
I can explain why DE ∥ BC makes ∠ADE ≅ ∠ABC and ∠AED ≅ ∠ACB, and conclude △ADE ~ △ABC by AA.
Requires: M5, M6
Grand Mastery Challenge
I can demonstrate independent mastery across classification, algebra, proof, and transfer without hints.
Requires: M13, M14, M15, M16