GEOMETRY Unit 5, Triangles Conjectures 5-4, Side/Angle Relationships

GEOMETRY Unit 5, Triangles Conjectures 5-4, Side/Angle Relationships

Side Length Conjecture

Open the GeoGebra applet for “GG-Triangle Side Lengths”. Adjust the sliders and the sides of the triangles as indicated below to answer the following questions:

1. a) Let side a = 11, side b = 3, and side c = 11. Can you make a triangle with these three side lengths? _____

b) Let side a = 11, side b = 3, and side c = 10. Can you make a triangle? ______

c) Let side a = 11, side b = 3, and side c = 9. Can you make a triangle? ______

d) Let side a = 11, side b = 3, and side c = 8. Can you make a triangle? ______

e) Let side a = 11, side b = 3, and side c = 7. Can you make a triangle? ______

2. a) Let side a = 8, side b = 5, and side c = 5. Can you make a triangle with these three side lengths? ______

b) Let side a = 8, side b = 5, and side c = 4. Can you make a triangle? ______

c) Let side a = 8, side b = 5, and side c = 3. Can you make a triangle? ______

d) Let side a = 8, side b = 5, and side c = 2. Can you make a triangle? ______

3. a) Let side a = 10, side b = 3, and side c = 7.3. Can you make a triangle with these three side lengths? ______

b) Let side a = 10, side b = 3, and side c = 7.2. Can you make a triangle? ______

c) Let side a = 10, side b = 3, and side c = 7.1. Can you make a triangle? ______

d) Let side a = 10, side b = 3, and side c = 7.0. Can you make a triangle? ______

e) Let side a = 10, side b = 3, and side c = 6.9. Can you make a triangle? ______

4. Write down three lengths that could be the sides of a triangle:

a = _____, b = ______, c = ______

5. Write down three lengths that could NOT be the sides of a triangle:

a = _____, b = ______, c = ______

Complete the following conjecture about the lengths of the sides of a triangle: Given line segments with lengths of a, b, and c, in order for the three lengths to make a triangle, ______

______.