[size=200][size=100][u]On a lined sheet of paper, record your responses to the following:[/u][br]1. If the red angle is the [b]largest[/b] angle then the _______ side is the longest side (you can use your mouse to change the shape of the triangle).[br]2. If the green angle is the [b]largest[/b] angle then the _______ side is the longest side.[br]3. If the blue angle is the [b]smallest [/b]angle then the _______ side is the shortest side.[br]4. If the red side is the [b]longest[/b] side then the _______ angle is the largest angle.[br]5. If the green side is the [b]shortest[/b] side, then the ______ angle is the smallest angle.[br]6. In conclusion, the ______ side will always be _______ from the ______ angle and the ______ side will always be _______ from the ______ angle. This is called the [u]Opposite Sides & Angles Theorem[/u]. It is on page 328 ( your book broke it into two theorems). Now would be a good time to add it to your Truth Bank.[br]7. In ΔXYZ, ∠Y is the smallest angle, so _____ must be the shortest side.[br]8. In ΔQRS, QR is the longest side. What can you conclude?[br][/size][size=100]9.[/size][size=100]In ΔTUV,[/size][size=100]∠U is the largest angle. What can you conclude?[br][/size][/size][br][size=100]10. [/size][size=100]In ΔHKJ, m[/size][size=100]∠K =125º, [size=100]m[/size][size=100]∠H =11º andHJ = 8 in. [br] a) What is [size=100]m[/size][size=100]∠J?[/size][br] b) Is KJ =, <, or > 8 in.?[/size][br][/size] c) Is HK =, <, or > 8 in?[br][br]11. [size=100]In ΔDEF, m[/size][size=100]∠D =80º, [size=100]m[/size][size=100]∠E =60º ,DE = 500 ft., and [/size][/size]EF = 800 ft.[br] a) What is [size=100]m[/size][size=100]∠F?[/size][br] b) List the angles in ΔDEF in order from smallest to largest.[br] c) List the sides of ΔDEF in order from shortest to longest.[br] d) What is the shortest that DF could be? What is the longest it could be?[br][br]12. In ΔPQR, PQ = 18m, QR = 26m, and PR = 18.5m. List the angles of ΔPQR in order from smallest to largest. [br][br]13. [size=100]In ΔLMN, m[/size][size=100]∠L =[math]10\frac{4}{5}[/math]º, and [size=100]m[/size][size=100]∠N =10.75º[/size][/size].[br] a) List the angles of ΔLMN in order from smallest to largest.[br] b) List the sides of ΔLMN in order from shortest to longest.[br][br][b]Check your answers before moving on to the next part.[/b]

It turns out that not every group of 3 segments can make a triangle. The goal of this next part is to discover what the pattern is.[br][br]14. Use the applet above. With AB=10, AC=4, and BC=7, is it possible to move the C points together to create a triangle?[br][br]15. Now use AB=10, AC=4, and BC=5.5. You should notice that it is impossible to create a triangle with these three segment lengths. Why is this? What could you change to make it work?[br][br]16. Now use AB=8, AC=3, and BC=1. These segments don't make a triangle either. Leave AB=8 and AC=3. How long do you have to make BC so that it can form a triangle? BC must be at least larger than _______. How does this number relate to the lengths of AB and AC?[br][br]17. Leave AB=8, and AC=3, but make BC = 15. This can't make a triangle either. Is BC too short or too long? In order to form a triangle, BC must be at least shorter than ________. How does this number relate to the lengths of AB and AC?[br][br]18. Now use AB=12 and AC = 5. In order to form a triangle, BC must be longer than _____ but shorter than ______. In other words: _____ < BC < ______.[br][br]19. Now use AB=3 and AC=6. In order to form a triangle, _____ < BC < _____.[br][br]20. Suppose AB=500 and AC=200. In order to form a triangle, _____ < BC < _____.[br][br]21. Let's write a rule that works for any AB and AC. In order to form a triangle with AB and AC, [br]____________ < BC < ____________. This is called the [u]Triangle Inequality Theorem.[/u] Now would be a good time to add it to your truth bank. Don't forget a picture!

Just incase you didn't get it with the last applet, here's another applet that demonstrates the same thing.[br]Notice that when you change AC and AB, the possibility for CB changes too.[br][br]22. If AC=3 and AB=10, then _____ < CB < _____.[br][br]23. If AC=12 and AB=3, then _____ < CB < _____.[br][br]24. If AC=7 and AB=7, then _____ < CB < _____.[br][br]25. If AC=482 and AB=900, then _____ < CB < _____.[br][br]26. If AC=[math]\frac{1}{2}[/math] and AB=[math]\frac{1}{4}[/math], then _____ < CB < _____.[br][br]27. If AC=[math]\frac{1}{2}[/math] and AB=[math]\frac{3}{8}[/math], then _____ < CB < _____.

Notice that in the above applet, the blue segments are congruent and the black segments are congruent. The blue and black segments also do not change length.[br][br]28. Notice that when you lengthen BE, what happens to ∠A?[br][br]29. If BE > DF, then what is true about angle A and angle C?[br][br]30. If m∠C > m∠A, then what is true about BE and DF?[br][br]31. Set BE=5. If DF > 5, then m∠C > _____.[br][br]32. Set m∠A=70. If m∠C < 70, then DF < _____.[br][br]33. In triangle QRS and triangle XYZ, QR=XY and RS=YZ. If QS > XZ, then what can you say about ∠R and ∠Y? (Drawing a picture might help).[br][br]34. This is called the [u]Hinge Theorem[/u]. It's in the green box on page 335 of your textbook (they broke it into two theorems). Now would be a good time to add this to your truth bank.[br][br]THE LAST SET OF QUESTIONS ARE FROM THE TEXTBOOK:[br][br]p331: 8,11-13,17-23[br]p338: 3-9[br]