From the given figure, let's prove that at least one air of triangles are congruent.
Here, let's assume the the shape at the middle is a square since the information was not given.
If it is a square, the white pair of triangles and also the red pair of triangles inside the square can be said to be congruent using the Side Angle Side (SAS) theorem.
The SAS theorem states that if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle, both triangles are congruent.
Here, the equal angles of both triangles can be said to be the vertical angles.
Vertical angles can be said to be a pair of opposite angles formed by intersecting lines.
From the figure below, the triangles congruent by SAS theorem are:
• Triangle AEB and triangle DEC are congruent by SAS
,
• Triangle AED and triangle BEC are congruent by SAS.
From the figure below the white triangles are congruent by SAS.
From the figure below, we can see the red triangles inside the square are also congruent by SAS theorem.
ANSWER:
SAS
• Triangle AEB and triangle DEC are congruent by SAS
,
• Triangle AED and triangle BEC are congruent by SAS.