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MAFS.912.G-CO.3.11 41. Write a proof of the theorem that states if an angle of a quadrilateral is supplementary to both of its consecutive angles, the quadrilateral is a parallelogram. Given: mzF + mZG = 180, mZF + m J = 180 Prove: FGHJ is a parallelogram What statement proves the theorem? A. By the Angle Addition Postulate mZF = m and mZG = mZH. So, by the definition of a parallelogram, FGHJ is a parallelogram. B. By the Converse of the Same-Side Interior Ang Postulate, FJ || GH and FG || JH . So, by t definition of a parallelogram, FGHJ is a parallelogram. C. By the Polygon Interior Angle-Sum Theorem + mZG + mZF + mZJ = 360, So, by the defin of a parallelogram, FGHJ is a parallelogram. D. By the Converse of the Same-Side Interior A Postulate, FJ = JH and FG = JH . So, by %3D definition of a parallelogram, FGHJ is a

MAFS.912.G-CO.3.11 41. Write a proof of the theorem that states if an angle of a quadrilateral is supplementary to both of its consecutive angles, the quadrilateral is a parallelogram. Given: mzF + mZG = 180, mZF + m J = 180 Prove: FGHJ is a parallelogram What statement proves the theorem? A. By the Angle Addition Postulate mZF = m and mZG = mZH. So, by the definition of a parallelogram, FGHJ is a parallelogram. B. By the Converse of the Same-Side Interior Ang Postulate, FJ || GH and FG || JH . So, by t definition of a parallelogram, FGHJ is a parallelogram. C. By the Polygon Interior Angle-Sum Theorem + mZG + mZF + mZJ = 360, So, by the defin of a parallelogram, FGHJ is a parallelogram. D. By the Converse of the Same-Side Interior A Postulate, FJ = JH and FG = JH . So, by %3D definition of a parallelogram, FGHJ is a

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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2. A. 1, 1I, IH B. I, I, C. I, IH D. II, V MAFS.912.G-CO.3.11 41. Write a proof of the theorem that states if an 42. Which angle of a quadrilateral is supplementary to both of its consecutive angles, the Given: A Prove: A quadrilateral is a parallelogram. Given: mZF + mZG = 180, %3D mZF + m J = 180 Prove: FGHJ is a parallelogram 1. A What statement proves the theorem? A. By the Angle Addition Postulate mZF = m and mZG = mZH. So, by the definition of a %3D parallelogram, FGHJ is a parallelogram. B. By the Converse of the Same-Side Interior Angles Postulate, FJ || GH and FG || JH.So, by the definition of a parallelogram, FGHJ is a parallelogram. C. By the Polygon Interior Angle-Sum Theorem, mZF + mZG+ mZF + mZJ = 360, So, by the definition %3D of a parallelogram, FGHJ is a parallelogram. D. By the Converse of the Same-Side Interior Angles Postulate, FJ = JH and FG = JH. So, by the %3D definition of a parallelogram, FGHJ is a narallelogram
Transcribed Image Text:2. A. 1, 1I, IH B. I, I, C. I, IH D. II, V MAFS.912.G-CO.3.11 41. Write a proof of the theorem that states if an 42. Which angle of a quadrilateral is supplementary to both of its consecutive angles, the Given: A Prove: A quadrilateral is a parallelogram. Given: mZF + mZG = 180, %3D mZF + m J = 180 Prove: FGHJ is a parallelogram 1. A What statement proves the theorem? A. By the Angle Addition Postulate mZF = m and mZG = mZH. So, by the definition of a %3D parallelogram, FGHJ is a parallelogram. B. By the Converse of the Same-Side Interior Angles Postulate, FJ || GH and FG || JH.So, by the definition of a parallelogram, FGHJ is a parallelogram. C. By the Polygon Interior Angle-Sum Theorem, mZF + mZG+ mZF + mZJ = 360, So, by the definition %3D of a parallelogram, FGHJ is a parallelogram. D. By the Converse of the Same-Side Interior Angles Postulate, FJ = JH and FG = JH. So, by the %3D definition of a parallelogram, FGHJ is a narallelogram
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