Geometry

Hong Kong

Stage 1 - Stage 3

In the diagram, $C$`C` is a point on $AD$`A``D` such that $AB\parallel CE$`A``B`∥`C``E` and $z=\angle BCD$`z`=∠`B``C``D`. $x$`x` and $y$`y` are two angles in $\triangle ABC$△`A``B``C`, 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

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 $AC$`A``C` bisects $\angle BAD$∠`B``A``D`, and $DE=EF$`D``E`=`E``F`. By letting $\angle CAD=x$∠`C``A``D`=`x` , prove that $AC$`A``C` is parallel to $DF$`D``F`.

In $\triangle ABC$△`A``B``C`, given $\angle ABC=\angle BAC+\angle ACB$∠`A``B``C`=∠`B``A``C`+∠`A``C``B`

prove that $\angle ABC=90$∠`A``B``C`=90

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