# Thread: New Question on congruency

1. ## New Question on congruency

Hi,

PQRS is a square and equilateral triangles PQA and RQB are drawn witgh A inside and B outside the square.

By considering triangles PQR and AQB, prove that AB is equal to PR.

Thankyouu very much

2. Originally Posted by doopers3
Hi,

PQRS is a square and equilateral triangles PQA and RQB are drawn witgh A inside and B outside the square.

By considering triangles PQR and AQB, prove that AB is equal to PR.

Thankyouu very much

The triangles are equilateral, so you know the angles in them are all 60. Specifically, $\angle PQA \cong \angle BQR$. Since this is true, you know that $m\angle RQA = 30$.

Can you use that fact to see some right triangles containing the segments you need to prove have equal measures? Be sure to draw yourself a decent picture so you can see them.