David uses software to draw two triangles. He finds that he can use a rotation and a reflection to map one triangle onto the other, and he finds that the image of vertex D is vertex L, the image of vertex V is vertex C, and the image of vertex W is vertex Y. In how many different ways can David write a congruence statement for the triangles? Complete the explanation.
Use the given information to select congruence statements.
△DVW ≅ △
△DWV ≅ △
△VDW ≅ △
△VWD ≅ △
△WDV ≅ △
△WVD ≅ △

There are more ways with the order of the triangles reversed. There is a total of ways to write a congruence statement.

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MrRoyal MrRoyal · Answer 1 · 2021-10-27T13:24:25+02:00

Transformation involves changing the position of a shape.

The complete statement is:

There are _3_ more ways with the order of the triangles reversed. There is a total of _9_ ways to write a congruence statement.

From the question, we understand that:

[tex]\mathbf{\triangle DVW \cong \triangle LCY}[/tex]

This mean that, the following 6 statements can be used as the congruent statements

[tex]\mathbf{\triangle DVW \cong \triangle LCY}[/tex]

[tex]\mathbf{\triangle DWV \cong \triangle LYC}[/tex]

[tex]\mathbf{\triangle VDW \cong \triangle CLY}[/tex]

[tex]\mathbf{\triangle VWD \cong \triangle CYL}[/tex]

[tex]\mathbf{\triangle WDV \cong \triangle YLC}[/tex]

[tex]\mathbf{\triangle WVD \cong \triangle YCL}[/tex]

A triangle has 3 sides, and there are 2 triangles in the question.

The number (n) of congruence statements is:

[tex]\mathbf{n = 3^2 = 9}[/tex]

The remaining (r) number of congruent statement is:

[tex]\mathbf{r = 9 - 6 = 3}[/tex]

So, the blanks should be completed with 3 and 9

Read more about congruent triangles at:

https://brainly.com/question/12413243