Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

Solution

This solution uses the inscribed angle theorem to show the top angles of the triangles are both 45°. Also it uses SAS to prove their congruence.

Please find here a nice animation by Amaresh G S showing all possibilities.

Visual solution

Poem

If we share our place
We have the same face
The triangles so sweet and small
Have to be patient first of all
Sometimes they try to say
Wanting to go out for freedom anyway
They share their colours too
1 twin is red the second blue
And listen so politely
Hello to you with glee

Bella