Geometry · Triangle Similarity Academy™
From angle relationships → similarity → proportionality → proof. Discover → Match → Justify → Prove → Solve → Transfer.
Learning map — prerequisite dependencies
Missions unlock as you visit their prerequisites. Progress conceptually, not in isolation.
Similarity Readiness Diagnostic
I can show readiness for similarity by recalling angles, ratios, and parallel-line angle theorems.
What Does Similar Mean?
I can state the two structural conditions that define triangle similarity.
Requires: M0
Corresponding Vertices
I can match corresponding vertices even when triangles are rotated or reflected.
Requires: M1
Writing Similarity Statements Correctly
I can write a similarity statement with vertices in corresponding order.
Requires: M2
Corresponding Angles
I can identify all three congruent corresponding angle pairs in similar triangles.
Requires: M3
Corresponding Sides
I can identify the three pairs of corresponding sides and use the ratio validator.
Requires: M4
Ratios and Proportionality
I can set up and solve a proportion between corresponding sides.
Requires: M5
Scale Factor
I can use a scale factor to relate corresponding sides, perimeter, and area.
Requires: M6
AA Similarity
I can prove triangles similar using the AA criterion and explain why two angles suffice.
Requires: M7, M4
SAS Similarity
I can prove triangles similar using SAS similarity, with the included angle condition.
Requires: M8
SSS Similarity
I can prove triangles similar using SSS similarity by checking all three ratios.
Requires: M9
Choose the Correct Similarity Criterion
I can select AA, SAS, SSS, or 'not enough info' from given evidence and justify it.
Requires: M8, M9, M10
Find Missing Angles
I can find a missing angle in similar triangles using the angle sum.
Find Missing Sides
I can find a missing side by confirming correspondence, then solving a proportion.
Requires: M6, M12
Parallel Lines Create Similar Triangles
I can prove △ADE ~ △ABC from DE ∥ BC using corresponding angles and AA.
Requires: M8, M11
Similarity Proof Laboratory
I can arrange a two-column proof of similarity with correct statement/reason order.
Requires: M14
Algebra + Similarity
I can solve multi-step algebra problems embedded in similarity proportions.
Requires: M13
Error Detective
I can locate the first incorrect step in flawed similarity reasoning and correct it.
Requires: M11, M16
Real-World Applications
I can model real-world situations with similar triangles and solve via proportions.
Mixed Challenge Laboratory
I can solve mixed similarity problems across criteria, correspondence, and scale factor.
Requires: M11, M13, M17
Grand Similarity Mastery Challenge
I can demonstrate mastery across all similarity dimensions with accumulated evidence.
Requires: M19