Congruent, similar or neither?
Compare ten pairs of figures, from a page and its photocopy to a small and a large map of Nepal. Check their sides and angles, and sort the pairs into congruent, similar or neither.
Core concept
Congruent figures have the same shape and the same size; similar figures have the same shape (equal angles, sides in the same ratio) but can be different sizes; every congruent pair is also similar
Topic: Congruent figures
Two figures are congruent if one fits exactly on top of the other: same shape and same size, like two coins of the same kind or a page and its photocopy. Their matching sides are equal and their matching angle: The amount of turn between two lines that meet, measured in degrees (°). All key words are equal. Two figures are similar if they have the same shape but maybe a different size, like a photo and its enlargement or two maps of Nepal at different scales. Their matching angles are equal and their matching sides are in the same ratio: A way to compare two amounts, like 2 cups of rice to 3 cups of water (2 : 3). All key words. A square and a long rectangle are neither: their angles match, but their sides are not in the same ratio.
What you will learn
- Define congruent and similar figures.
- Decide whether two figures are congruent, similar or neither by their sides and angles.
- Give everyday examples of congruent and similar figures.
Before you start
- Know how to measure sides and angles.
Materials
- Two coins of the same kind, a photo and its enlargement, tracing paper
Equipment
- A ruler and a protractor
Procedure
- Pick a pair and compare their sides and their angles.
- Do this for at least six pairs.
- Sort every pair.