IXL - Proofs involving the Triangle Midsegment Theorem (Geometry practice)

is the midpoint of

and

is the midpoint of

Complete the proof that

∥

	Statement	Reason
1	W is the midpoint of segmentsegmentSV	Given
2	T is the midpoint of segmentsegmentSU	Given
3	segmentSW equals segmentSV/2	Definition of midpoint
4	segmentST equals segmentSU/2	Definition of midpoint
5	segmentSW/segmentSV equals 1/2	Properties of addition, subtraction, multiplication, and division
6	segmentST/segmentSU equals 1/2	Properties of addition, subtraction, multiplication, and division
7	segmentST/segmentSU equals segmentSW/segmentSV	Transitive Property of Equality
8	∠S is congruent to ∠S	Reflexive Property of Congruence
9	△STW is similar to △SUV
10	∠STW is congruent to ∠U	Definition of similarity
11	segmentsegmentTW is parallel to segmentsegmentUV	Converse of Corresponding Angles Theorem

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Learn with an example

is the midpoint of

and

is the midpoint of

Complete the proof that

∥

	Statement	Reason
1	Y is the midpoint of segmentsegmentUX	Given
2	V is the midpoint of segmentsegmentUW	Given
3	segmentUY equals segmentUX/2	Definition of midpoint
4	segmentUV equals segmentUW/2	Definition of midpoint
5	segmentUY/segmentUX equals 1/2	Properties of addition, subtraction, multiplication, and division
6	segmentUV/segmentUW equals 1/2	Properties of addition, subtraction, multiplication, and division
7	segmentUV/segmentUW equals segmentUY/segmentUX	Transitive Property of Equality
8	∠U is congruent to ∠U	Reflexive Property of Congruence
9	△UVY is similar to △UWX	Text field with dropdown. Use the down arrow key to hear the options, press spacebar to select.
10	∠UVY is congruent to ∠W	Definition of similarity
11	segmentsegmentWX is parallel to segmentsegmentVY	Converse of Corresponding Angles Theorem

Choose the reason that justifies the statement on line 9. The SAS Similarity Theorem lets you deduce

△

from

in line 7 and

∠

≅

∠

in line 8.

	Statement	Reason
1	Y is the midpoint of segmentsegmentUX	Given
2	V is the midpoint of segmentsegmentUW	Given
3	segmentUY equals segmentUX/2	Definition of midpoint
4	segmentUV equals segmentUW/2	Definition of midpoint
5	segmentUY/segmentUX equals 1/2	Properties of addition, subtraction, multiplication, and division
6	segmentUV/segmentUW equals 1/2	Properties of addition, subtraction, multiplication, and division
7	segmentUV/segmentUW equals segmentUY/segmentUX	Transitive Property of Equality
8	∠U is congruent to ∠U	Reflexive Property of Congruence
9	△UVY is similar to △UWX	SAS Similarity
10	∠UVY is congruent to ∠W	Definition of similarity
11	segmentsegmentWX is parallel to segmentsegmentVY	Converse of Corresponding Angles Theorem

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