Question

Given △ABC, AD and BE are medians, AD ∩BE=G. Prove: GD/AG = DE/AB

Answer 1

Answer:

See explanantion

Step-by-step explanation:

Since AD and BE are medians, then points D and E are midpoints of the sides BC and AC, respectively. Thus, segment DE is triangle's midline. By the Triangle midline theorem, DE is parallel to the side AB. Thus,

• $\angle ABE\cong \angle BED;$
• $\angle BAD\cong \angle EDA$

as alternate interior angles.

Moreover, $\angle BGA\cong \angle EGD$ as vertical angles.

This gives us that triangles ABG and DEG are similar by AAA postulate.

Hence,

$\dfrac{AB}{ED}=\dfrac{AG}{GD}$