Both the larger and the smaller squares are formed by two triangles of the same size.
The green and red triangles are the same size. Similarly, the orange and yellow triangles are also of the same size. We can create this figure using copies of two different-sized triangles.
△ ABC≅△ CDA
Let's use colors to indicate the corresponding sides. We need to show that the segments with the same color are congruent.
The table below contains the segment congruence statements and the reasons why that statement is true.
Segment Congruence
Justification
AB≅ CD
The sides of the square ABCD are congruent.
BC≅ DA
The sides of the square ABCD are congruent.
CA≅ AC
Any segment is congruent to itself (reflexive property of congruence).
Since three sides of triangle â–³ ABC are congruent to three sides of triangle â–³ CDA, the Side-Side-Side (SSS) Congruence Postulate guarantees that the triangles are congruent.
c
Since ABCD is a square, line BC is perpendicular to both AB and CD.
