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22. Given: 4I 2 Prove: a. AJIG AJZY JG GI b. JY YZ Y

22. Given: 4I 2 Prove: a. AJIG AJZY JG GI b. JY YZ Y

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.
Chapter10: Analytic Geometry
Section10.4: Analytic Proofs
Problem 19E: Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of...
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This is a geometry question.
**Problem 22** **Given:** ∠1 ≅ ∠2 **Prove:** a. ΔJIG ~ ΔJZY b. \(\frac{JG}{JY} = \frac{GI}{YZ}\) **Diagram Explanation:** There is a triangle JZY with the following elements: - Points: J, I, G, Y, Z - One smaller triangle (JIG) is inside the larger triangle (JZY). - A line intersects the base JY at point G, creating a segment JG within the base. - Angles are indicated inside the triangles, one at point Z and one at point I, both labeled similarly. According to the information, ∠1 and ∠2 are congruent. The congruency of these angles can be used to prove that the triangles ΔJIG and ΔJZY are similar and that the ratio of the segments JG to JY equals the ratio of the segments GI to YZ.
Transcribed Image Text:**Problem 22** **Given:** ∠1 ≅ ∠2 **Prove:** a. ΔJIG ~ ΔJZY b. \(\frac{JG}{JY} = \frac{GI}{YZ}\) **Diagram Explanation:** There is a triangle JZY with the following elements: - Points: J, I, G, Y, Z - One smaller triangle (JIG) is inside the larger triangle (JZY). - A line intersects the base JY at point G, creating a segment JG within the base. - Angles are indicated inside the triangles, one at point Z and one at point I, both labeled similarly. According to the information, ∠1 and ∠2 are congruent. The congruency of these angles can be used to prove that the triangles ΔJIG and ΔJZY are similar and that the ratio of the segments JG to JY equals the ratio of the segments GI to YZ.
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