#Winter Life Check-in Season#The basics and improvements of grade 8 are shown in the figure. In triangle ABC, AC=7, BC=4, D is the midpoint of AB, E is the point on AC, and angle AED=90 degrees + 1/2 angle C, find the length of CE. Analysis: 1) Angle AED=90 degrees + 1/2 angle C

2025/09/2522:26:34 education 1205

Analysis: 1) Angle AED=90 degrees + 1/2 Angle C is the breakthrough. We first extend the ED CB, and they intersect with M. If we pass C to perform CP vertical EM, we can get the angle CEP=1/2 Angle C, indicating that CP is the angle bisector of angle C. Thus, we get the triangle ECM is an isosceles triangle, CE=CM! (angle CEM=CME=AEN)

Suppose CE=CM=x, then BM=x-4

2) via A to make the AN parallel CM cross DE extension line at N

Angle CEM=CME=ANE=AEN

So AE=AN=7-x

AD=DB

triangle ADN congruent MBD

BM=AN x-4=7-xx x=11/2

Summary: We constructed isosceles triangle ECM through complement and constructed isosceles triangle AEN in parallel. By proving that ADN and BDM are congruent triangle . Finally, we concluded that CE=11/2.

Improvement: How to prove sine theorem

a:sinA=b:sinB=c:sinC?

How to use the sine theorem to find this question?

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