Question

Am I doing this right?

The triangle ABC in the figure below has midpoints labeled M and N and O.



complete the following transformation

Answer 1

Yes you are right. Notice how the midpoint also create another triangle, a lot of geometry is symmetry

Answer 2

2). B

Explanation:

We have been given a triangle ABC, whose midpoints are M, N and O. We are asked to complete the given transformation.

`H_M{\circ}H_O:C\rightarrow`

The midpoint theorem states that segment connecting the midpoints of two sides of a triangle is parallel to third side and half the measure of third side. By midpoint theorem:

`\overline{MN}=\overline{AO}=\overline{OC}`

`\overline{ON}=\overline{AM}=\overline{MB}`

`\overline{MO}=\overline{BN}=\overline{NC}`

We can see that by joining midpoints, we get 4 congruent triangles:

`\Delta MN\cong \Delta MAO\cong \Delta ONM \cong \Delta NOC`

We can also see that midpoint M corresponds to vertex C, so midpoint O will correspond to vertex B.

Therefore our required transformation would be
`H_M{\circ}H_O:C\rightarrow B` and 2nd option is the correct choice.