Common Core · High school
HSG-SRT.B.5
High school — Use congruence and similarity criteria for triangles to solve problems and prove relationships.
High school — Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
The 3 skills that cover it
- Similar TrianglesRecognise similar figures, write proportions between corresponding sides, and use them to find unknown lengths.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 →
- Similar Solids & Composite FiguresScale the area and volume of similar figures by the square and cube of the scale factor, find the area of regular polygons, and measure composite figures and cross-sections of solids.Read the lesson →
What a student should be able to do
- Identify similar triangles from angle relationships.
- Write and solve a proportion between corresponding sides, including the side-splitter, midsegment and angle-bisector theorems.
- Use a scale factor to find perimeters and areas.
- Solve indirect measurement problems such as shadow heights.
- 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.
- Relate the scale factor of similar solids to the ratio of their surface areas and volumes.
- Find the area of a regular polygon from its apothem and perimeter.
- Find the area or volume of a composite figure by splitting it into known pieces.
- Identify the cross-section of a solid and use density in a measurement problem.