The following proof of the Pythagorean Theorem is attributed to the Thābit ibn Qurra (836–901) and is recounted by Heath. B F A Figure 7.36. Exercise 7.6.7: Thābit ibn Qurra's proof of the Pythagorean Theorem Let AABC be given with right angle at A. Construct square DABDE on side AB; produce AC to F such that EF = AC. Construct square DEHGF on side EF, and produce DH to K such that DK = AC , as illustrated in Figure 7.36. (a) Prove that triangles ABAC, ACCFG,AKHG and ABDK are all congruent. (b) Prove that quadrilateral BCGK is a square. (c) Decompose DABDE and DEFGH into nonoverlapping pieces that, when rear- ranged, form square BCGK. Explain why this proves the Pythagorean Theo- rem.
The following proof of the Pythagorean Theorem is attributed to the Thābit ibn Qurra (836–901) and is recounted by Heath. B F A Figure 7.36. Exercise 7.6.7: Thābit ibn Qurra's proof of the Pythagorean Theorem Let AABC be given with right angle at A. Construct square DABDE on side AB; produce AC to F such that EF = AC. Construct square DEHGF on side EF, and produce DH to K such that DK = AC , as illustrated in Figure 7.36. (a) Prove that triangles ABAC, ACCFG,AKHG and ABDK are all congruent. (b) Prove that quadrilateral BCGK is a square. (c) Decompose DABDE and DEFGH into nonoverlapping pieces that, when rear- ranged, form square BCGK. Explain why this proves the Pythagorean Theo- rem.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![The following proof of the Pythagorean Theorem is attributed to the Thābit ibn Qurra (836–901) and is recounted by Heath.
![Diagram of triangles and squares involved in Thabit ibn Qurra's proof of the Pythagorean Theorem.]
*Figure 7.36. Exercise 7.6.7: Thābit ibn Qurra’s proof of the Pythagorean Theorem*
Let \( \triangle ABC \) be given with right angle at \( A \). Construct square \( \square ABDE \) on side \( AB \); produce \( AC \) to \( F \) such that \( EF = AC \). Construct square \( \square EHGF \) on side \( EF \), and produce \( DH \) to \( K \) such that \( DK = AC \), as illustrated in Figure 7.36.
(a) Prove that triangles \( \triangle BAC \), \( \triangle CFG \), \( \triangle KHG \), and \( \triangle BDK \) are all congruent.
(b) Prove that quadrilateral \( BCGK \) is a square.
(c) Decompose \( \square ABDE \) and \( \square EFGH \) into nonoverlapping pieces that, when rearranged, form square \( \square BCGK \). Explain why this proves the Pythagorean Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93507587-8486-4bd1-9be9-7c1c5dc70b2a%2F0b1e0ae5-ebb8-4286-8808-b6a8b075ab7b%2Fio7jjnvl_processed.png&w=3840&q=75)
Transcribed Image Text:The following proof of the Pythagorean Theorem is attributed to the Thābit ibn Qurra (836–901) and is recounted by Heath.
![Diagram of triangles and squares involved in Thabit ibn Qurra's proof of the Pythagorean Theorem.]
*Figure 7.36. Exercise 7.6.7: Thābit ibn Qurra’s proof of the Pythagorean Theorem*
Let \( \triangle ABC \) be given with right angle at \( A \). Construct square \( \square ABDE \) on side \( AB \); produce \( AC \) to \( F \) such that \( EF = AC \). Construct square \( \square EHGF \) on side \( EF \), and produce \( DH \) to \( K \) such that \( DK = AC \), as illustrated in Figure 7.36.
(a) Prove that triangles \( \triangle BAC \), \( \triangle CFG \), \( \triangle KHG \), and \( \triangle BDK \) are all congruent.
(b) Prove that quadrilateral \( BCGK \) is a square.
(c) Decompose \( \square ABDE \) and \( \square EFGH \) into nonoverlapping pieces that, when rearranged, form square \( \square BCGK \). Explain why this proves the Pythagorean Theorem.
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