Geometry
Hong Kong
Stage 1 - Stage 3
Proofs with Triangles
Interactive practice questions
In the diagram, $C$C is a point on $AD$AD such that $AB\parallel CE$AB∥CE and $z=\angle BCD$z=∠BCD. $x$x and $y$y are two angles in $\triangle ABC$△ABC, as labelled. Prove that the sum of the two interior angles of the triangle equals the exterior angle. That is, prove that $x+y=z$x+y=z.
Easy
4min
Show that the exterior angles in a triangle add up to $360^\circ$360° by showing that $x+y+z=360$x+y+z=360.
Easy
5min
In the diagram $AC$AC bisects $\angle BAD$∠BAD, and $DE=EF$DE=EF. By letting $\angle CAD=x$∠CAD=x , prove that $AC$AC is parallel to $DF$DF.
Easy
8min
In $\triangle ABC$△ABC, given $\angle ABC=\angle BAC+\angle ACB$∠ABC=∠BAC+∠ACB
prove that $\angle ABC=90$∠ABC=90
Easy
3min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account