Question

1. do you remember what makes each of the following triangles special?

a. isosceles triangle
b. equilateral triangle
c. scalene triangle
d. right triangle
e. acute triangle
f. obtuse triangle

1. review suppose points a, b, and c are collinear, where b is between a and c. if ab = 2x + 3, bc = 6x - 5, and ac = 22, solve for x.

Explanation:

Step1: Use the segment - addition postulate

Since \(A\), \(B\), and \(C\) are collinear and \(B\) is between \(A\) and \(C\), we have \(AB + BC=AC\).
Substitute \(AB = 2x + 3\), \(BC = 6x-5\), and \(AC = 22\) into the equation: \((2x + 3)+(6x - 5)=22\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+6x+3 - 5=22\), which simplifies to \(8x-2 = 22\).

Step3: Solve for \(x\)

Add \(2\) to both sides of the equation: \(8x-2 + 2=22 + 2\), so \(8x=24\).
Divide both sides by \(8\): \(x=\frac{24}{8}\).

Answer:

\(x = 3\)