3. Prove that angle 1= angle 2, so angle 1 ACE= angle 2 ACE, so angle ACB= angle DCE.

In triangle ACB and triangle DCE, CA=CD, angle ACB= angle DCE, BC=EC.

Triangle ACB is all equal to triangle DCE(SAS).

So DE=AB

4. It is proved that because angle CAD= angle CBD, angle CBA= angle DAB, and triangle CAB AB=AB are all equal to triangle DBA(ASA), the distances between islands C and D and the coasts where observation points A and B are located are equal.

5. Prove: Because DE is perpendicular to AB, DF is perpendicular to AC, angular bed = angle CFD = 90, BD=CD because D is the midpoint of BC.

In Rt triangular bed and Rt triangular CFD, BD = CD and BE = CF, so Rt triangular bed is equal to Rt triangular CFD(HL).

So DE=DF, so AD is the bisector of triangle ABC.

Because these three roads form a triangle, they should be built on the bisector of the three sides of the triangle.

Review questions 12

1.

leave out

3.① Ab2be3 asymmetry ④C is 3 units away from the X axis, and E is 2 units away from the X axis.

4. Angle D = 25 Angle E = 40 Angle DAE = 1 15.

5. It is proved that AE = CE and AD = BD because D and E are the midpoint of AB and AC respectively, CD is perpendicular to AB, and D is perpendicular to AC and E..

So angle BEA= angle CDA=90. In triangle BEA and triangle CDA, angle BEA= angle CDA, AE=AD, angle A= angle A, so.

Triangle BEA is equal to triangle CDA(ASA), so AC=AB.

It is proved that in triangle DAB and triangle CBA, AB=AB, AD=BC, BD=AC, so triangle DAB is equal to triangle CBA(SSS), so angle CAB= angle DAB, so AE=BE, so triangle EAB is an isosceles triangle.

7. Proof: Because the angle A = 30, the CD is high and the angle ACB=90, so ∠ ACD = 60 = ∠ B ∠ BCD = 30, so BD= 1/2CB CB= 1/2AB.