Question

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.

Answer 1

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:

$\mathbf{\triangle DVW \cong \triangle LCY}$

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

$\mathbf{\triangle DVW \cong \triangle LCY}$

$\mathbf{\triangle DWV \cong \triangle LYC}$

$\mathbf{\triangle VDW \cong \triangle CLY}$

$\mathbf{\triangle VWD \cong \triangle CYL}$

$\mathbf{\triangle WDV \cong \triangle YLC}$

$\mathbf{\triangle WVD \cong \triangle YCL}$

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

The number (n) of congruence statements is:

$\mathbf{n = 3^2 = 9}$

The remaining (r) number of congruent statement is:

$\mathbf{r = 9 - 6 = 3}$

So, the blanks should be completed with 3 and 9

Read more about congruent triangles at:

brainly.com/question/12413243