Objective- To use the Third Side Property to find the third side of a triangle given the other two. 5 ft. 7 ft. X What could the value of x be?
Could the value of x be 100? 5 ft. 7 ft. X X= 100 ft. No, that would be ridiculous! The other two sides would never meet.
What is the maximum value x could be? 5 ft. 7 ft. X
What is the maximum value x could be? 5 ft. 7 ft. X
What is the maximum value x could be? 5 ft. 7 ft. X
What is the maximum value x could be? 5 ft. 7 ft. X
What is the maximum value x could be? 5 ft. 7 ft. X
What is the maximum value x could be? 5 ft. 7 ft. X The value of x is now 12, but is this a triangle?
No this is not a triangle, it is a straight line No this is not a triangle, it is a straight line. The triangle has collapsed. 5 ft. 7 ft. X If x = 12 the sides will make a line. If x > 12 the sides will not touch. Therefore, x < 12. or X < 5 + 7
Triangle Inequality a b X x < a + b or a + b > x
Triangle Inequality The sum of any two sides must always be larger than a third side Which could be the sides of a triangle? 1) 7 8 10 Yes 2) 2 6 8 No 3) 4 12 17 No 4) 6 15 3 No
Is there a limit to how small x could be? 5 ft. 7 ft. X Obviously, x could not be a negative number or 0. In order to be a distance, it must be a positive real number.
Could x = 1? 5 ft. 7 ft. X 7 ft. 5 ft. X=1 No, The third side would be too small.
What is the smallest value for x? 7 ft. 5 ft. X Could the value of x be 2?
Once again, this would be impossible as it would create a straight line. 7 ft. 5 ft. X=2 x simply must be greater than 2 in order to create a triangle.
So, x has both a maximum value and a minimum value So, x has both a maximum value and a minimum value. We call this the Third Side Property. 5 ft. 7 ft. X 7 - 5 < x < 7 + 5 Or...
< < Third Side Property The third side of a triangle must be between the sum and the difference of the other two sides. Difference of the other two sides Sum of the other two sides Third Side < <
What are the possible values of x? 12 15 x 15 - 12 < x < 12 + 15 3 < x < 27
What are the possible values of x? 9 13 x 13 - 9 < x < 9 + 13 4 < x < 22
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Farthest Case = 16 miles A B C 6 miles 10 miles
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Less than 16 Miles A B C 6 miles 10 miles
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Less than 16 Miles A B 6 miles 10 miles C
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Less than 16 Miles A B 6 miles 10 miles C
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Less than 16 Miles A B 6 miles 10 miles C
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Less than 16 Miles A B 6 miles 10 miles C
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Less than 16 Miles A B 6 miles 10 miles C
Related Problem Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Less than 16 Miles A B 6 miles 10 miles C
Related Problem 4 x 16 Alice lives 6 miles from Betty. Carla lives 10 miles from Betty. How far could Alice and Carla live apart? Shortest Case = 4 Miles A B 4 Miles 6 miles C 10 miles 4 x 16