Constructions and congruence
Explain constructions and identify corresponding sides and angles using congruence.
Meaning
A construction uses specified tools and rules to make a figure satisfying conditions. Congruent figures coincide after moving or reflecting, with equal corresponding lengths and angles.
Example
Two triangles with sides 3 cm, 4 cm, and 5 cm are congruent by equal corresponding sides. Equal angles alone can leave different sizes. First match the 5 cm sides. The remaining vertex must be 3 cm from one endpoint and 4 cm from the other. The two possible circle intersections are reflections across that side, so reflection makes the triangles coincide. Distinguish triangle congruence from similarity. Matching angles alone does not establish equal size.
Practice for this concept
Scope and references
Topics
Basic constructions, triangle congruence conditions, corresponding sides and angles
Learning goal
Explain constructions and identify corresponding sides and angles using congruence.
Helpful background
Explore segments, angles, perpendiculars, and parallels.
Construction and congruence
These choice exercises use stated geometric conditions. They do not establish construction, drawing, spatial manipulation, written proof, or mastery of the whole geometry area.