I’m sure you have seen some of the figure which in one way or another one of the shape can become another using turns, flip or slide. These shapes are said to be Congruent. Study this notes carefully to know different ways that can help you to recognize congruent figures.
In geometry two figures or objects are congruent if they have the same shape and size, or if one has the shape and size as the mirror image of the other.
If one shape can become another using turns (rotation), flip (reflection), and/ or slide (translation), then the shapes are Congruent. After any of these transformations the shape must still have the same size, perimeters, angles, areas and line lengths.
Note that; the two shapes need to be the size to be Congruent i.e. only rotation, reflection and/ or translation is needed.
- Two line segments are Congruent if they have the same length.
- Two angles are Congruent if they have the same measure.
- Two circles are Congruent if they have the same diameter.
- They are Congruent: vertical angles are always of equal measure i.e. a = b, and c = d.
- Sum of vertical angles (all four angles) is 3600 i.e. a + b + c + d =3600
- Sum of Adjacent angles (angles from each pair) is 1800 i.e. a + d =1800 ; a + c =1800 ; c + b =1800 ; b + d =1800.
Congruence of Triangles
- READ TOPIC 6: Similarity