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Proofs with Triangles

Interactive practice questions

In the diagram, $C$C is a point on $AD$AD such that $AB\parallel CE$ABCE 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.

Approx 4 minutes

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.

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.

In $\triangle ABC$ABC, given $\angle ABC=\angle BAC+\angle ACB$ABC=BAC+ACB

prove that $\angle ABC=90$ABC=90

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