Ruler and Compass, proofs

Use the three congruence theorems, the theorem about isosceles triangles and the theorems about angles to prove that the constructions 1-7 are correct.

Hint: Place triangles in appropriate ways into the constructions.

Example, Construction 1 Bisect angle

You must show that the angles BAC and CAD are equal.

Mark the triangles ΔABC and ΔACD.

Use one of the congruence theorems to show that the triangles are congruent. Justify that you can use this theorem.

Show that the angles BAC and CAD are equal.

Example, Construction 2 Bisect segment

You must show that the segments AE and EB are equal.

Show this for the angles: DAB=DBA=CAB=CBA.

Then show this for the angles: BDC=ADC=ACD=BCD .

Show that ΔAED≅ΔBED!