Proportions in Triangles Practice

Name: Class: Date: Practice Form G Proportions in Triangles Use the figure at the right to complete each proportion. 1. a/c = d/f 2. f/c = c/b 3. b/c = g/f 4. a/d = b/e 5. a/b = d/e 6. b/e = g/f Algebra: Solve for x. 7. x = 6 8. x = 5 9. x = 7 10. x = 5 11. x = 5 12. x = 3 13. x = 12 14. x = 2 15. x = 12 16. x = 2 17. x = 3 18. x = 6 Practice (continued) Proportions in Triangles 19. Compare and Contrast How is the Triangle-Angle-Bisector Theorem similar to Corollary 2 of Theorem   62? How is it different? Answers may vary. Sample: Both relate to a line that intercepts an angle of a triangle and its opposite side. In both, the segments created by the intersecting line are related proportionally to the sides of the triangle. Corollary 2 of Theorem   62 is only true of right triangles with an altitude to the hypotenuse. The Triangle-Angle-Bisector Theorem relates to all triangles that contain an angle bisector that intersects the opposite side. 20. Reasoning   In △FGH, the bisector of ∠F also bisects the opposite side. The ratio of each half of the bisected side to each of the other sides is 1:2. What type of triangle is   △FGH? Explain. △FGH is an equilateral triangle. Because the side has been bisected, each segment is the same length. So, their sum is: x+x=2x. This is the same as the length of a side. 21. Error Analysis Your classmate says you can use the Triangle-Angle-Bisector Theorem to find the value of x in the diagram. Explain what is wrong with your classmate's statement.   [Image of a triangle with sides labeled] The classmate is confusing this Theorem with Corollary 1 to Theorem 62. You could only find the value of x if △FHI were a right triangle with right ∠I, and ‾IG were an altitude to the hypotenuse. 22. Reasoning An angle bisector of a triangle divides the opposite side of the triangle into segments 3 in. and 6 in. long. A second   side of the triangle is 5 in. long. Find the length of the third side of the triangle. Explain how you arrived at the correct length.   10 in.; The other possible side length is 2.5 in., but because 2.5 in. + 5 in. < 9 in., it violates the Triangle Inequality Theorem.   23. The flag of Antigua and Barbuda is like the image at the right. In the image, DE || CF || BG. a. An artist has made a sketch of the flag for a mural. The measures indicate the length of the lines in feet. What is the value of x? 4   [Image of a flag with labeled sides] b. What type of triangle is △ACF? Explain. △ACF is isosceles. Because x = 4, CB ≅ FG and BA ≅ GA. Because CA = CB + BA and FA = FG + GA, by substitution CA ≅ FA. c. Given: DE || CF || BG Prove: △ABG ~ △ACF ~ △ADE [Image of a flag with labeled sides] Statements: 1) DE || CF || BG; 2) ∠EDC ≅ ∠FCB ≅ ∠GBA; 3) ∠DEF ≅ ∠CFG ≅ ∠BGA; 4) △ABG ~ △ACF ~ △ADE; Reasons: 1) Given; 2) If lines are ||, corresponding ∠s are ≅; 3) If lines are ||, corresponding ∠s are ≅; 4) AA~