IXL - Prove the Pythagorean theorem (Geometry practice)

Complete the proof that

	Statement	Reason
1	segmentsegmentGH is perpendicular to segmentsegmentFH	Given
2	segmentsegmentEH is perpendicular to segmentsegmentFG	Given
3	∠FHG is congruent to ∠GEH	All right angles are congruent
4	∠G is congruent to ∠G	Reflexive Property of Congruence
5	△FGH is similar to △HGE	AA Similarity
6	segmentEG/segmentGH equals segmentGH/segmentFG	Definition of similarity
7	segmentFG times segmentEG equals expression with exponent	Properties of addition, subtraction, multiplication, and division
8	∠FHG is congruent to ∠FEH	All right angles are congruent
9	∠F is congruent to ∠F	Reflexive Property of Congruence
10	△FGH is similar to △FHE	AA Similarity
11	segmentEF/segmentFH equals segmentFH/segmentFG
12	segmentFG times segmentEF equals expression with exponent	Properties of addition, subtraction, multiplication, and division
13	segmentFG(segmentEG plus segmentEF) equals expression with exponent plus expression with exponent	Properties of addition, subtraction, multiplication, and division
14	segmentFG equals segmentEG plus segmentEF	Additive Property of Length
15	expression with exponent plus expression with exponent equals expression with exponent	Substitution

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Learn with an example

Complete the proof that

	Statement	Reason
1	segmentsegmentRS is perpendicular to segmentsegmentQR	Given
2	segmentsegmentRT is perpendicular to segmentsegmentQS	Given
3	∠QRS is congruent to ∠RTS	Text field with dropdown. Use the down arrow key to hear the options, press spacebar to select.
4	∠S is congruent to ∠S	Reflexive Property of Congruence
5	△QRS is similar to △RTS	AA Similarity
6	segmentST/segmentRS equals segmentRS/segmentQS	Definition of similarity
7	segmentQS times segmentST equals expression with exponent	Properties of addition, subtraction, multiplication, and division
8	∠QRS is congruent to ∠QTR	All right angles are congruent
9	∠Q is congruent to ∠Q	Reflexive Property of Congruence
10	△QRS is similar to △QTR	AA Similarity
11	segmentQT/segmentQR equals segmentQR/segmentQS	Definition of similarity
12	segmentQS times segmentQT equals expression with exponent	Properties of addition, subtraction, multiplication, and division
13	segmentQS(segmentST plus segmentQT) equals expression with exponent plus expression with exponent	Properties of addition, subtraction, multiplication, and division
14	segmentQS equals segmentST plus segmentQT	Additive Property of Length
15	expression with exponent plus expression with exponent equals expression with exponent	Substitution

Choose the reason that justifies the statement on line 3. The fact that all right angles are congruent lets you deduce

∠

QRS

≅

∠

RTS

from

⟂

in line 1 and

⟂

in line 2.

	Statement	Reason
1	segmentsegmentRS is perpendicular to segmentsegmentQR	Given
2	segmentsegmentRT is perpendicular to segmentsegmentQS	Given
3	∠QRS is congruent to ∠RTS	All right angles are congruent
4	∠S is congruent to ∠S	Reflexive Property of Congruence
5	△QRS is similar to △RTS	AA Similarity
6	segmentST/segmentRS equals segmentRS/segmentQS	Definition of similarity
7	segmentQS times segmentST equals expression with exponent	Properties of addition, subtraction, multiplication, and division
8	∠QRS is congruent to ∠QTR	All right angles are congruent
9	∠Q is congruent to ∠Q	Reflexive Property of Congruence
10	△QRS is similar to △QTR	AA Similarity
11	segmentQT/segmentQR equals segmentQR/segmentQS	Definition of similarity
12	segmentQS times segmentQT equals expression with exponent	Properties of addition, subtraction, multiplication, and division
13	segmentQS(segmentST plus segmentQT) equals expression with exponent plus expression with exponent	Properties of addition, subtraction, multiplication, and division
14	segmentQS equals segmentST plus segmentQT	Additive Property of Length
15	expression with exponent plus expression with exponent equals expression with exponent	Substitution

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