Question

Verify segment sr ≅ segment yx and segment st ≅ segment yz by translation. Verify ∠s ≅ ∠y and ∠t ≅ ∠z by reflection. Verify segment sr ≅ segment yx and segment st ≅ segment yz by reflection. Verify ∠s ≅ ∠y and ∠t ≅ ∠z by translation.

Answer 1

To verify congruence of line segments and angles by translation and reflection.

Step-by-step explanation:

To verify the congruence of the line segments SR and YX by translation, we need to show that the coordinates in S' are expressed in terms of the coordinates in S using the rotation transformation formulas:

x' = x cos(q) + y sin(o)

y' = -x sin(p) + y cos(p)

Similarly, to verify the congruence of the line segments ST and YZ by translation, we can use the same rotation transformation formulas. To verify the congruence of the angles S and Y by reflection, we can show that the angles are equal in measure. Similarly, to verify the congruence of the angles T and Z by reflection, we can show that the angles are equal in measure.

Therefore, by using translation and reflection, we can verify the congruence of the line segments SR ≅ YX and ST ≅ YZ, as well as the angles S ≅ Y and T ≅ Z.