Given: pq= tq, uq: qs

prove: ps tu

reasons

statements

1. pq= to, uq= os

2. pq = tq, uq = qs

3. pq+ qs = ps; tq + qu = tu

4. tq + qs = ps

5. tq + qs = tu

6. ps = tu

7. ps = tu

1. given

2. reflexive ž

3. addition poe

4. seament addition post

5. seament addition post

6. u

7. definition of congroencel

gina wilson (all things algebra), 2014

The required prove is shown below.

Step-by-step explanation:

Consider the provided statement.

The required figure is shown below:

 Statement                                             Reasons

PQ ≅ TQ; UQ ≅ QS                               Given

PQ = TQ, UQ = QS                     Definition of Congruence

PQ + QS = PS; TQ+QU = TU    Segment Addition Postulate

TQ + QS = PS                            Substitution  (PQ = TQ)

TQ + QS = TU                            Substitution  (QU = QS)

PS = TU                                    Transitive Property

Prove: PS ≅TU                          Definition of Congruence

Hence, the required prove is shown above.

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