Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Congruence criteria for triangles
Justify triangle congruence with transformations and criteria
Problem types
- Select the corresponding parts of congruent triangles
- Congruence by rigid motions
- Which givens fix the triangle?
- Prove SAS, ASA or SSS with rigid motions
- Justify a step of a rigid-motion congruence proof
- Find the flaw in a rigid-motion congruence proof
- Prove six congruent parts give a rigid motion
- Reason from the definition of congruence
- Build the rigid motion between two triangles
- Write a two-column triangle congruence proof
Builds on
- Writing and critiquing a geometric proof
- Translations, reflections, and rotations
- When given measures make a triangle · Useful idea
Three given sides or angles that fix a triangle's shape are the conditions behind the congruence criteria.
- Sides, angles, and faces · Earlier idea
Telling congruent figures from near copies by their sides and corners is the informal idea that congruence criteria later make exact for triangles.
Leads to
- Proofs about parallelograms
- Proofs about triangles
- Deriving the laws of sines and cosines · See it applied
The measurements that determine a triangle by congruence criteria are the measurements the laws of sines and cosines can solve for.
Related skills
- Theorems about circles · Shared foundations
- Proofs that use coordinates · Shared foundations
- Dilations and similarity · Shared foundations
- Proofs about lines and angles · Shared foundations
- Why the circle and solid formulas hold · Shared foundations
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