Question

complete problems 25, 27, 28, 31, and 32 for independent practice.
when you are finished, check the solutions with your teacher.
copy and complete the proof. (see example 1.)

1. given: ( pq = rs )

prove: ( pr = qs )
statements reasons

1. ( pq = rs ) 1.
2. ( pq + qr = rs + qr ) 2.
3. ( pq + qr = pr ) 3.
4. ( rs + qr = qs ) 4.
5. ( pr = qs ) 5.

reasons bank: addition property of equality, segment addition postulate (× 2), transitive property, given
name the property that the statement illustrates.

1. if ( overline{pq} cong overline{st} ) and ( overline{st} cong overline{uv} ), then ( overline{pq} cong overline{uv} ).
2. ( angle f cong angle f )
3. if ( overline{xy} cong overline{uv} ), then ( overline{uv} cong overline{xy} ).
4. if ( angle l cong angle m ) and ( angle m cong angle n ), then ( angle l cong angle n ).

property bank:
reflexive property of segment congruence, reflexive property of angle congruence
symmetric property of segment congruence, symmetric property of angle congruence
transitive property of segment congruence, transitive property of angle congruence

Explanation:

Step1: Match given statement reason

Statement 1: $PQ = RS$ is the given information.
Reason 1: Given

Step2: Match equality addition reason

Statement 2: $PQ + QR = RS + QR$ uses adding the same segment to both sides.
Reason 2: Addition Property of Equality

Step3: Match segment addition reason

Statement 3: $PQ + QR = PR$ follows the segment addition postulate.
Reason 3: Segment Addition Postulate

Step4: Match segment addition reason

Statement 4: $RS + QR = QS$ follows the segment addition postulate.
Reason 4: Segment Addition Postulate

Step5: Match transitive equality reason

Statement 5: $PR = QS$ uses substituting equal expressions.
Reason 5: Transitive Property

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Step6: Identify 27's congruence property

$\overline{PQ} \cong \overline{ST}$ and $\overline{ST} \cong \overline{UV}$ implies $\overline{PQ} \cong \overline{UV}$: Transitive Property of Segment Congruence

Step7: Identify 28's congruence property

$\angle F \cong \angle F$: Reflexive Property of Angle Congruence

Step8: Identify 31's congruence property

$\overline{XY} \cong \overline{UV}$ implies $\overline{UV} \cong \overline{XY}$: Symmetric Property of Segment Congruence

Step9: Identify 32's congruence property

$\angle L \cong \angle M$ and $\angle M \cong \angle N$ implies $\angle L \cong \angle N$: Transitive Property of Angle Congruence

Answer:

Problem 25 Proof Completion:

STATEMENTS	REASONS
2. $PQ + QR = RS + QR$	2. Addition Property of Equality
3. $PQ + QR = PR$	3. Segment Addition Postulate
4. $RS + QR = QS$	4. Segment Addition Postulate
5. $PR = QS$	5. Transitive Property

Problem 27:

Transitive Property of Segment Congruence

Problem 28:

Reflexive Property of Angle Congruence

Problem 31:

Symmetric Property of Segment Congruence

Problem 32:

Transitive Property of Angle Congruence