Congruence and Similarity

Congruence means identical; similarity means scaled identical. Two photos of same size = congruent. Original and enlargement = similar. Indirect aim: preparation for trigonometry, map-making, scale models.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Geometry
• Level: Ages 8-10

Objectives

• Define congruent (same shape and size) vs similar (same shape, scaled)
• Identify congruent and similar figures
• Use ratios to find scale factors
• Apply to maps and models

Materials

• Congruent figure pairs
• Similar figure pairs
• Ruler, protractor
• Maps with scale

Instructions

1. Compare two congruent triangles: same angles, same sides. 2. Compare similar triangles: same angles, sides in ratio. 3. Measure: if big triangle sides are 2x small, that's the scale factor. 4. Apply to maps (1:100,000). 5. Compute distances. 6. Build similar shapes on grid paper. 7. Study: all squares are similar; all circles are similar. 8. File.

Educator tip

Similar triangles are trigonometry's foundation. Children who master this are ready for SOHCAHTOA in a year or two.

Assessment

Observe correct identification, ratio computation, and scale application.

More from Mathematics

• Geometric Symmetry — Reflection, Rotation, Translation
• Measurement — Length in Metric
• Measurement — Weight and Mass
• Measurement — Capacity and Volume
• Measurement — Time and Calendar
• Measurement — Temperature and Thermometry
• Algebra — Simplifying Expressions
• Algebra — Solving Multi-Step Equations