Question

given: $overline{pq}congoverline{tq},overline{uq}congoverline{qs}$
prove: $overline{ps}congoverline{tu}$

statements\treasons

1. $overline{pq}congoverline{tq},overline{uq}congoverline{qs}$\t1.
2. $pq = tq,uq = qs$\t2.
3. $pq + qs=ps;tq + qu = tu$\t3.
4. $tq + qs = ps$\t4.
5. $tq + qs = tu$\t5.
6. $ps = tu$\t6.
7. $overline{ps}congoverline{tu}$\t7.

Explanation:

Step1: State given information

Given

Step2: Use definition of congruent segments

Def. of congruent segments

Step3: Use segment - addition postulate

Segment - addition postulate

Step4: Substitute PQ for TQ

Substitution property

Step5: Substitute UQ for QS

Substitution property

Step6: Transitive property of equality

Transitive prop. of equality

Step7: Use definition of congruent segments

Def. of congruent segments

Answer:

1. Given
2. Def. of congruent segments
3. Segment - addition postulate
4. Substitution property
5. Substitution property
6. Transitive prop. of equality
7. Def. of congruent segments