Common Core · High school
HSG-CO.C.10
High school — Prove theorems about triangles.
The 2 skills that cover it
- Logic & ProofRead a conditional statement, write its converse, inverse and contrapositive, test a claim with a counterexample, and give the reason for every step of a proof.Read the lesson →
- Triangle CongruenceDecide when two triangles are congruent from the SSS, SAS, ASA, AAS and HL criteria, match corresponding parts, and supply the missing statement or reason in a congruence proof.Read the lesson →
What a student should be able to do
- Identify the hypothesis and conclusion of a conditional statement.
- Write the converse, inverse and contrapositive and decide which are true.
- Use a counterexample, the law of detachment and the law of syllogism to test reasoning.
- Justify each step of an algebraic or geometric proof with a definition, property, postulate or theorem.
- Match corresponding sides and angles of congruent triangles from a congruence statement.
- Choose the criterion (SSS, SAS, ASA, AAS or HL) that proves two triangles congruent, or decide there is not enough information.
- Use CPCTC to find an unknown side or angle once triangles are congruent.
- Supply the missing statement or reason in a two-column congruence proof.