Midpoint theorem (triangle): Difference between revisions

Revision as of 07:20, 17 September 2024

Revision as of 07:30, 17 September 2024

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Therefore, <math>\frac{AB}{DE}=\frac{AC}{DC}=\frac{BC}{EC}=2,</math> which means that <math>DE=\frac{1}{2}AB.</math>

Since <math>\triangle ABC</math> and <math>\triangle DEC</math> are similar, <math>\angle CDE = \angle CAB</math>, which means that <math>AB\parallel DE</math>.

Since <math>\frac{AB}{DE}=\frac{AC}{DC}=\frac{BC}{EC},</math> DE is parallel to AB by [[Intercept theorem]].

[[Q.E.D.]]