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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 …

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