Congurence & Similarity

Congurency:

Two geometric figures are congurent, if they are of the same shape and size.

                                                                                 AB =XY               ∠a = ∠x

BC = YZ               ∠b = ∠y

AC = XZ               ∠c = ∠z

Tests of Congurency:

• Side Side Side (SSS) – all sides are equal
• Angle Angle Angle (AAA) – all angles are same
• Side Angle Side (SAS) – two sides and one angle are equal
• Right Angled – Hypotenuse – Side – one right angle and hyp & side equal

≡  – To denote “ is congruent to”

≢ – To denote “ is not congruent to”

Similarity:

When two figures are similar, they are exactl the same in shape but not in size.

Test:

• Equal corresponding Angles:

The angles of one triangle are equal to corresponding angles of the other triangle.

• Proportional Corresponding Angles.
• Two Pairs of Proportional Corresponding Sides with equal angles.

We right similarity as ( ~ ) i.e ΔABC ~ ΔDEF

Ratios of Area And Volumes:

Same Ratio:

Ratio of Area:

Ratio of Volume: