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Consider triangle PQR with line segment ST parallel to line segment QR. R The table shows a proof that line segment ST, parallel to line segment QR, divides the sides of the triangle proportionally. Step Statement Reason 1 ST I QR 1. Given 2 LP LP 2. Reflexive Property 3 ZPST = LPQR, and ZPTS E LPRQ 3. 4 APST is similar to APQR. 4. AA similarity PQ PR 5. PS PT 6. Substitution; Sis a point on the line segment PQ, and Tis a point on the line segment PR. PS + SQ PT + TR %3D PS PT SQ = 1 + PS TR 1+ 7. Separating the parts of the numerators PT sQ_ TR PS PT 8. Subtracting 1 from both sides

Consider triangle PQR with line segment ST parallel to line segment QR. R The table shows a proof that line segment ST, parallel to line segment QR, divides the sides of the triangle proportionally. Step Statement Reason 1 ST I QR 1. Given 2 LP LP 2. Reflexive Property 3 ZPST = LPQR, and ZPTS E LPRQ 3. 4 APST is similar to APQR. 4. AA similarity PQ PR 5. PS PT 6. Substitution; Sis a point on the line segment PQ, and Tis a point on the line segment PR. PS + SQ PT + TR %3D PS PT SQ = 1 + PS TR 1+ 7. Separating the parts of the numerators PT sQ_ TR PS PT 8. Subtracting 1 from both sides

Elementary Geometry For College Students, 7e
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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cricket ? 8:41 PM 5% Consider triangle PQR with line segment ST parallel to line segment QR. S T R The table shows a proof that line segment ST, parallel to line segment QR, divides the sides of the triangle proportionally. Step Statement Reason ST |I QR 1. Given 2 ZPE LP 2. Reflexive Property 3 ZPST = LPQR, and <PTS= LPRQ 3. 4 APST is similar to APQR. 4. AA similarity PQ PR 5. PS PT PS + SQ РТ + TR 6. Substitution; Sis a point on the line segment PQ, and Tis a point on the line segment PR. 6. %3D PS PT SQ 1+ =1 + PS TR 7 7. Separating the parts of the numerators PT SQ TR 8 8. Subtracting 1 from both sides %3D PS PT AA A student.masteryconnect.com C
Transcribed Image Text:cricket ? 8:41 PM 5% Consider triangle PQR with line segment ST parallel to line segment QR. S T R The table shows a proof that line segment ST, parallel to line segment QR, divides the sides of the triangle proportionally. Step Statement Reason ST |I QR 1. Given 2 ZPE LP 2. Reflexive Property 3 ZPST = LPQR, and <PTS= LPRQ 3. 4 APST is similar to APQR. 4. AA similarity PQ PR 5. PS PT PS + SQ РТ + TR 6. Substitution; Sis a point on the line segment PQ, and Tis a point on the line segment PR. 6. %3D PS PT SQ 1+ =1 + PS TR 7 7. Separating the parts of the numerators PT SQ TR 8 8. Subtracting 1 from both sides %3D PS PT AA A student.masteryconnect.com C
cricket ? 8:41 PM 5% Which are the correct reasons for Step 3 and Step 5? Reason 3: Alternate interior angles are equal. Reason 5: Corresponding sides of similar triangles are equal. Reason 3: Corresponding angles are equal. Reason 5: Corresponding sides of similar triangles are equal. Reason 3: Alternate interior angles are equal. Reason 5: Corresponding sides of similar triangles are proportional. Reason 3: Corresponding angles are equal. Reason 5: Corresponding sides of similar triangles are proportional. AA A student.masteryconnect.com C
Transcribed Image Text:cricket ? 8:41 PM 5% Which are the correct reasons for Step 3 and Step 5? Reason 3: Alternate interior angles are equal. Reason 5: Corresponding sides of similar triangles are equal. Reason 3: Corresponding angles are equal. Reason 5: Corresponding sides of similar triangles are equal. Reason 3: Alternate interior angles are equal. Reason 5: Corresponding sides of similar triangles are proportional. Reason 3: Corresponding angles are equal. Reason 5: Corresponding sides of similar triangles are proportional. AA A student.masteryconnect.com C
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