4.) The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What can you conclude about AC in ABC? (example guideline and problem are attached) 4. BC + AC = 22; AB + BC = 12%3D%3D Geometry The sum of the lengths of any two sides of a triangle is greater than the length of the thirdside. In AABC, BC = 4 and AC = 8- AB. What can you conclude about AB? AABC has three sides,so you can use the Triangle Inequality Theorem and write 3 conditions of the sides.%3DAC + BC > AB1st Triangle Inequality conditionAB + BC > AC2nd Triangle Inequality conditionAB + AC > BC3rd Triangle Inequality conditionBC = 4 and AC = 8- ABGiven(8- AB) + 4 > ABSubstitute 4 for BC and 8- AB for AC in the 1st condition.12 > 2ABSolve and simplify.AB < 6AB + 4 > 8 – ABSubstitute 4 for BC and 8- AB for AC in the 2nd condition.2AB > 4Solve and simplify.AB > 2AB + (8 - AB) > 4Substitute 4 for BC and 8- AB for AC in the 3rd condition.8 > 4Simplify. True Statement.2 < AB < 6Conclusion about AB.

Given △ABC with, BC+AC=22 -(1)AB+BC=12 -(2) Subtracting (2) from (1), we have:…

Answered: The sum of the lengths of any two sides…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter5: Linear Inequalities

Section5.4: Solving Compound Inqualities

Problem 36PPS

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4.) The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What can you conclude about AC in ABC? (example guideline and problem are attached)

Geometry The sum of the lengths of any two sides of a triangle is greater than the length of the third
side. In AABC, BC = 4 and AC = 8- AB. What can you conclude about AB? AABC has three sides,
so you can use the Triangle Inequality Theorem and write 3 conditions of the sides.
%3D
AC + BC > AB
1st Triangle Inequality condition
AB + BC > AC
2nd Triangle Inequality condition
AB + AC > BC
3rd Triangle Inequality condition
BC = 4 and AC = 8- AB
Given
(8- AB) + 4 > AB
Substitute 4 for BC and 8- AB for AC in the 1st condition.
12 > 2AB
Solve and simplify.
AB < 6
AB + 4 > 8 – AB
Substitute 4 for BC and 8- AB for AC in the 2nd condition.
2AB > 4
Solve and simplify.
AB > 2
AB + (8 - AB) > 4
Substitute 4 for BC and 8- AB for AC in the 3rd condition.
8 > 4
Simplify. True Statement.
2 < AB < 6
Conclusion about AB.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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