1, (1) 35,35 (2) 80,20 or 50,50.

2. Proof: ∫ AD//BC ∴ ADB = ∠ DBC, while ∫BD shares ∠ABC ∴∠ABD=∠DBC.

∴∠ADB =∞ Abdul ∴ AB = AD (equiangular to opposite side, and so on. )

3. Solution: ∵ All five angles of the five-pointed star are isosceles triangles with the top angle of 36, ∴ The degree of each bottom angle is

( 1/2)×( 180-36)= 72 ,∴∠amb= 180-72 = 108

4. Solution: ab = ac, ∴∠ BAC = 100, ∴∠ B = ∠ C = (1/2) × (180-6568).

And ∵AD⊥BC, ∴AD is the bisector of ∠BAC, ∴∠ bad = ∠ CAD = (1/2) ×100 = 50.

5. Proof: ∫ce//ad, ∴ A = ∠ CEB, while ∫a =∠b, ∴ A = ∠ CEB = ∠ B, ∴ CE =

△ CBE is an isosceles triangle.

6. Proof: ∫ab = AC ∴∠b=∠c∫ad = AE, ∴∠ADE=∠AED ∴∠ADB=∠AEC.

In △ABD and △ACE, ∠ B = ∠ C, ∠ ADB = ∠ AEC ∴△ Abd △ Ace (AAS).

∴BD=CE (the corresponding sides of congruent triangles are equal)