if ab=12,bc=7,and ac=19 what must be true of points a,b and c
They are all on the same line.
Ac=19Units
AB+BC= 12+7=19
So if your draw them all out on the same line AC=19 Units
AB=5x+2
AC=3x+17
To determine what must be true about points A, B, and C, we need to use the given information about the lengths of the line segments AB, BC, and AC.
Given:
AB = 12
BC = 7
AC = 19
We can make the following conclusions:
1. AB + BC = AC (Triangle Inequality Theorem):
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If AB + BC = AC, it means that the segments AB, BC, and AC can form a triangle.
In this case:
12 + 7 = 19
19 = 19
So, the given lengths satisfy the Triangle Inequality Theorem, which means points A, B, and C can form a triangle.
2. AB + BC > AC:
If AB + BC is greater than AC, it indicates that the triangle ABC is an acute triangle (all angles are less than 90 degrees).
In this case:
12 + 7 = 19
19 > 19
Since AB + BC is equal to AC, the triangle ABC is not an acute triangle.
3. AB + BC < AC:
If AB + BC is less than AC, it indicates that the triangle ABC is an obtuse triangle (one angle is greater than 90 degrees).
In this case:
12 + 7 = 19
19 < 19
Since AB + BC is equal to AC, the triangle ABC is not an obtuse triangle.
In conclusion, based on the given lengths, we can determine that the points A, B, and C can form a triangle, but we cannot determine whether it is acute or obtuse without knowing the angles.