Properties of Equality and Congruence Worksheet with Answer Key

What's on the worksheet

1. Name the property or definition that allows each step.
   PQ = 2x and PQ + QR = 30, so 2x + QR = 30m\angle 1 = m\angle 2, so 3 \cdot m\angle 1 = 3 \cdot m\angle 2\overline{GH} \cong \overline{JK}, so GH = JKXY = ZW, so XY - 6 = ZW - 6m\angle 4 = m\angle 5, so m\angle 5 = m\angle 4
2. Write the statement for each line of a solution when only the reasons survived.
3. Use congruent segments and expressions to find x and a length.
4. Explain why dividing by x was wrong in Owen's solution, and find every solution.
5. Decide whether each relation is reflexive, symmetric and transitive.
6. Prove that segments AC and CE are congruent from given points on a line.