Question

question 6 of 10
the segments shown below could form a triangle.
a
c
b
4
3
6
c
b
a
a. true
b. false

Explanation:

Step1: Recall 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. Let the side - lengths be \(a = 3\), \(b = 4\), and \(c = 6\).

Step2: Check the first inequality

Check \(a + b>c\). Substitute \(a = 3\), \(b = 4\), and \(c = 6\). We get \(3 + 4=7>6\).

Step3: Check the second inequality

Check \(a + c>b\). Substitute \(a = 3\), \(c = 6\), and \(b = 4\). We get \(3+6 = 9>4\).

Step4: Check the third inequality

Check \(b + c>a\). Substitute \(b = 4\), \(c = 6\), and \(a = 3\). We get \(4 + 6=10>3\).

Answer:

A. True