Problem
GEO-B1-M01-P009 When a Triangle Is Right-Angled
#9
★★☆☆☆ Level 2 of 5
In a triangle, one angle is equal to the sum of the other two. Prove that the triangle is right-angled.
Let the two other angles be \(x\) and \(y\). Then the third angle is \(x+y\).
Let two angles be \(x\) and \(y\), and the third be \(x+y\). The angle sum gives \(x+y+(x+y)=180^\circ\). Therefore \(2(x+y)=180^\circ\), so \(x+y=90^\circ\). The third angle is \(90^\circ\), hence the triangle is right-angled.
This short proof is useful for moving from computations to proofs.