Geometric Twins

Congruent figures have the same shape and size. Four tests (SSS, SAS, ASA, RHS) show two triangles are congruent, so their matching parts are equal.

Key ideas

Congruent figures fit exactly on each other; matching sides and matching angles are equal.
SSS: all three sides equal. SAS: two sides and the angle between them equal.
ASA: two angles and the side between them equal. RHS: right angle, hypotenuse and one side equal.
Two sides and an angle that is not between them (SSA) is not enough, and nor are three equal angles (AAA).
Write congruent triangles with the matching vertices in the same order: △ABC ≅ △PQR means A ↔ P, B ↔ Q, C ↔ R.
Once triangles are congruent, all their matching parts are equal; a shared side counts for both triangles.

Tests	SSS, SAS, ASA, RHS
Not tests	SSA, AAA
Isosceles triangle	equal sides ⇔ equal opposite angles

Using SAS when the angle is not between the two sides.
Writing the vertices in an order that does not match.
Thinking triangles with equal angles must be congruent (they may be different sizes).

In kite ABCD, AB = AD = 7 cm and CB = CD = 12 cm. ∠BAC = 47°. Find ∠DAC and give the reason.

Working: △ABC ≅ △ADC by SSS (AC is shared), so the matching angles are equal

Answer: 47°