As shown in the figure, put two vertices of a right-angle triangular ruler with an angle of 30 on both sides of the paper ABCD, and measure ∠ FEA = 25, ∠ EGC = 35, ∠ A = 90. Is AB perpendicular to BC? And explain why.

answer

analyse

Carefully examine the questions, carefully observe the known conditions and given figures in the analysis questions, and solve them according to the judgment and properties of parallel lines and the theorem of triangle internal angle sum.

answer

Solution: AB⊥BC. The reasons are as follows:

∠∠EGF = 30，∠F=90

∴∠feg=90-∠ Epidermal growth factor =90 -30 =60

∠∠FEA = 25

∴∠AEG=∠FEG-∠FEA=60 -25 =35

∠∠EGC = 35

∴∠AEG=∠EGC

∴AD//BC

∠∠A = 90°

∴∠b= 180-∠a = 180-90 = 90

That's AB⊥BC.

So the answer is:

AB⊥BC.

comment

The key to solve this problem is to carefully examine the problem, carefully observe the known conditions and given figures in the analysis problem, and solve it according to the judgment and properties of parallel lines and the theorem of triangle interior angle sum.