Question

Danielle finds that she can use a translation and a reflection to make quadrilateral abcd fit perfectly on top of quadrilateral wxyz. What congruence statements can danielle write using the sides and angles of the quadrilaterals

Answer 1

The sequence of rigid motions maps with ABCD to WXYZ.

Also maps with sides and angles of ABCD to the corresponding sides and angles of WXYZ.

Therefore, those sides and angles are congruent.

`\bar{AB} \cong \bar{WX}, \bar{BC} \cong \bar{XY},`
`\bar{CD} \cong \bar{YZ},  \bar{AD} \cong \bar{WZ}`

`\angle A \cong \angle W`

`\angle B \cong \angle X`

`\angle C \cong \angle Y`

`\angle D \cong \angle Z`

Thus, the required solution is found.