## Solve Lesson 45 Page 92 SBT Math 10 – Kite>

Topic

Given two triangles ABC and A’B’C’ having the same focus is WOOD. Prove $$\overrightarrow {AA’} + \overrightarrow {BB’} + \overrightarrow {CC’} = \overrightarrow 0$$

Solution method – See details

Using the triangle centroid property, the 3-point rule (take WOOD is the intermediate point) to transform $$\overrightarrow {AA’} + \overrightarrow {BB’} + \overrightarrow {CC’}$$ and then conclude

Detailed explanation

Do WOOD is the centroid of the triangle ABC and triangle A’B’C’ should: $$\left\{ \begin{array}{l}\overrightarrow {GA} + \overrightarrow {GB} + \overrightarrow {GC} = \overrightarrow 0 \\\overrightarrow {GA’} + \overrightarrow {GB ‘} + \overrightarrow {GC’} = \overrightarrow 0 \end{array} \right.$$

We have: $$\overrightarrow {AA’} + \overrightarrow {BB’} + \overrightarrow {CC’} = \overrightarrow {GA’} – \overrightarrow {GA} + \overrightarrow {GB’} – \overrightarrow {GB } + \overrightarrow {GC’} – \overrightarrow {GC}$$

$$= \left( {\overrightarrow {GA’} + \overrightarrow {GB’} + \overrightarrow {GC’} } \right) – \left( {\overrightarrow {GA} + \overrightarrow {GB} + \overrightarrow {GC} } \right)$$$$= \overrightarrow 0 – \overrightarrow 0 = \overrightarrow 0$$