Congruent Triangles

• Similar and Congruent Figures
  • Two geometric figures having the same shape and size are said to be congruent figures.
  • Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.

Example: 

(1) All circles are similar.

(2) All equilateral triangles are similar.

(3) All congruent figures are similar. However, the converse is not true.

 

• Similarity of Polygons 

Two polygons with the same number of sides are similar, if

• • their corresponding angles are equal
  • their corresponding sides are in the same ratio (or proportion)

• Two lines segments are congruent, if they are equal in length.
• Two angles are congruent, if they have the same measure.
• CPCT:

CPCT stands for Corresponding Parts of Congruent Triangles. 

If ΔABC ΔPQR, then corresponding sides are equal i.e., AB = PQ, BC = QR, and CA = RP and corresponding angles are equal i.e., ∠A …