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7. Given AXPS = ADNF, find the values of r and v. P F 41-3 54 51 17x + 3 57

7. Given AXPS = ADNF, find the values of r and v. P F 41-3 54 51 17x + 3 57

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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## Problem Set on Congruent Triangles ### Problem 7 **Given**: △XPS ≅ △DNF **Task**: Find the values of x and y. **Diagram Explanation**: - Triangle XPS and Triangle DNF are congruent. - Angle relation: ∠X = 41° - 3, ∠P = 17x + 3, ∠S given as a value to be calculated. - Angles in △DNF: ∠D = 51°, ∠N = 57°, and ∠F = 54°. ### Problem 8 **Given**: △MTW ≅ △BGK **Task**: Find the values of x and y. **Diagram Explanation**: - Triangle MTW and Triangle BGK are congruent. - Angles in △MTW: ∠T = 43x - 3°, ∠M = value not provided, ∠W = 41°. - Angles in △BGK: ∠B = 45°, ∠G = 2y + 4° and ∠K = (11y - 6)°. ### Problem 9 **Given**: △PRS ≅ △CFH **Task**: Find the values of x, y, and z. **Diagram Explanation**: - Triangle PRS and Triangle CFH are congruent. - Side & angles in △PRS: ∠P = 28°, ∠R = (13y - 1)°, and side PS = 2y - 7. - Side & angles in △CFH: side CF = 24, ∠C = 39°, and angle FH = (6z - 4). In each problem, the congruency of triangles implies that corresponding sides and angles are equal, allowing you to equate them to solve for the variables.
Transcribed Image Text:## Problem Set on Congruent Triangles ### Problem 7 **Given**: △XPS ≅ △DNF **Task**: Find the values of x and y. **Diagram Explanation**: - Triangle XPS and Triangle DNF are congruent. - Angle relation: ∠X = 41° - 3, ∠P = 17x + 3, ∠S given as a value to be calculated. - Angles in △DNF: ∠D = 51°, ∠N = 57°, and ∠F = 54°. ### Problem 8 **Given**: △MTW ≅ △BGK **Task**: Find the values of x and y. **Diagram Explanation**: - Triangle MTW and Triangle BGK are congruent. - Angles in △MTW: ∠T = 43x - 3°, ∠M = value not provided, ∠W = 41°. - Angles in △BGK: ∠B = 45°, ∠G = 2y + 4° and ∠K = (11y - 6)°. ### Problem 9 **Given**: △PRS ≅ △CFH **Task**: Find the values of x, y, and z. **Diagram Explanation**: - Triangle PRS and Triangle CFH are congruent. - Side & angles in △PRS: ∠P = 28°, ∠R = (13y - 1)°, and side PS = 2y - 7. - Side & angles in △CFH: side CF = 24, ∠C = 39°, and angle FH = (6z - 4). In each problem, the congruency of triangles implies that corresponding sides and angles are equal, allowing you to equate them to solve for the variables.
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