Using the known properties of circles, like the fact that their radii are all equal, it is easy to solve geometry problems that require proof that triangles in the circle are congruent, like this one.
Problem
Two circles, with centers O and Q, intersect at points A and B. prove that △OAQ≅△OBQ.
Strategy
One of the sides of these two triangles, the line segment OQ which connects both centers, is common to both triangles.
The hint as to which other parts we should use to show the congruency is that these triangles were formed by the intersection of two circles- and the other two sides of both triangles are radii of the circles, which are equal to each other.
So the triangles are congruent using the Side-Side-Side postulate.
Proof
(1) OQ=OQ //Common side, reflexive property of equality
(2) QA=QB //Both are radii of circle Q, a circle’s radii are equal to each other
(3) OA=OB //Both are radii of circle O, a circle’s radii are equal to each other
(4) △OAQ≅△OBQ //Side-Side-Side postulate.