Properties of Parallelogram and Triangle Vectors
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Exercise IV: Consider a triangle $ABC$. 1. Construct the point $D$ so that $ABCD$ is a parallelogram. 2. Locate the point $E$ so that $\vec{AE} = \vec{AB} + \vec{AD}$. 3. Verify that $\vec{ED} = \vec{DC}$. 4. What does $[BD]$ represent in the triangle $BCE$?
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Hi Lilo, let's solve this geometry exercise involving vectors and parallelograms together.
First, we start with a triangle A B C. We need to construct point D such that A B C D is a parallelogram. In a parallelogram, opposite sides are equal and parallel.
1. Construction of Point D
For A B C D to be a parallelogram, vector A B must equal vector D C. This means D is located such that the quadrilateral forms that parallel shape.
In the second part, we locate point E such that vector A E equals vector A B plus vector A D.
2. Locate Point E
By the parallelogram law of vector addition, if A E is the sum of vectors A B and A D, then A B E D forms a parallelogram with A E as its diagonal.
We complete the parallelogram A B E D. Point E will be at the tip of the diagonal starting from A.
ABED ext{ is a parallelogram.}
Now for step three, let's verify that vector E D equals vector D C.
3. Verify \_overrightarrow{ED} = \_overrightarrow{DC}
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