Question

7 triangle efg is shown. using a ruler marked in centimeters: (a) locate and mark the midpoints of each side of triangle efg. (b) connect the midpoints using line - segments. (c) measure the length of each of the line segments you drew in (b) and label on the diagram. (d) what do you notice about these side lengths?

Explanation:

Step1: Locate mid - points

Use the ruler to find the mid - point of each side of $\triangle EFG$. For a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$, the mid - point formula is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2})$, but here we use the ruler to measure the length of each side and mark the middle point.

Step2: Connect mid - points

Draw line segments to connect the mid - points of the sides of the triangle.

Step3: Measure lengths

Use the ruler to measure the lengths of the newly - drawn line segments and label them on the diagram.

Step4: Analyze lengths

We notice that each of the line segments connecting the mid - points of the sides of the triangle is half the length of the side of the original triangle to which it is parallel. This is a property of the mid - segment theorem in geometry.

Answer:

(a) Mid - points are located and marked on each side of $\triangle EFG$ using a ruler.
(b) Mid - points are connected with line segments.
(c) Lengths of the line segments are measured and labeled on the diagram.
(d) Each line segment connecting mid - points is half the length of the parallel side of the original triangle.