IXL - Proofs involving parallel lines I (Geometry practice)

∠

UVX

and

∠

QSR

are supplementary. Complete the proof that

∥

	Statement	Reason
1	∠UVX and ∠QSR are supplementary	Given
2	measure of angle UVX plus measure of angle QSR equals 180 degrees	Definition of supplementary angles
3	measure of angle QSR plus measure of angle RSV equals 180 degrees	Angles forming a linear pair sum to 180 degrees
4	measure of angle UVX plus measure of angle QSR equals measure of angle QSR plus measure of angle RSV	Transitive Property of Equality
5	measure of angle UVX equals measure of angle RSV	Properties of addition, subtraction, multiplication, and division
6	segmentlineRT is parallel to segmentlineUW

ref_doc_title.

Learn with an example

question

Complete the proof that

∠

TUW

∠

PRQ

180°

	Statement	Reason
1	segmentlineQS is parallel to segmentlineTV	Given
2	∠TUW is congruent to ∠QRU	Corresponding Angles Theorem
3	measure of angle PRQ plus measure of angle QRU equals 180 degrees	Angles forming a linear pair sum to 180 degrees
4	measure of angle TUW plus measure of angle PRQ equals 180 degrees	Text field with dropdown. Use the down arrow key to hear the options, press spacebar to select.

solution

Choose the reason that justifies the statement on line 4. Substitution lets you deduce

∠

TUW

∠

PRQ

180°

from

∠

TUW

≅

∠

QRU

in line 2 and

∠

PRQ

∠

QRU

180°

in line 3.

	Statement	Reason
1	segmentlineQS is parallel to segmentlineTV	Given
2	∠TUW is congruent to ∠QRU	Corresponding Angles Theorem
3	measure of angle PRQ plus measure of angle QRU equals 180 degrees	Angles forming a linear pair sum to 180 degrees
4	measure of angle TUW plus measure of angle PRQ equals 180 degrees	Substitution

Looking for more? Try these:

Lesson: Transversals of parallel lines

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

D.4Transversals of parallel lines: find angle measures

C.9Proofs involving angles

Lesson: Transversals of parallel lines

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!