Question

esson 2.3.1/2.3.2 triangle inequality & pythagorean thm. name shyla kelly

1. (2 - 106) review: geometry

lines p and q on the graph at the right form a triangle with the x - axis.
a. how can you describe this triangle? in other words, what is the most appropriate name for this triangle? how do you know?
b. find the area of the triangle. a = \frac{1}{2}bh=
______un² or sq: un.

Explanation:

Step1: Identify the type of triangle

By observing the graph, if one of the angles formed by the intersection of lines \(p\), \(q\) and the \(x -\)axis is a right - angle (90 degrees), we can use the slope of the lines. If the product of the slopes of two lines is - 1, they are perpendicular. However, if we visually inspect the triangle and assume we can see a right - angle, this is a right - triangle.

Step2: Find the base and height for area calculation

Count the grid units on the graph. Let the base \(b\) be the length along the \(x -\)axis between the intersection points of lines \(p\), \(q\) with the \(x -\)axis and the height \(h\) be the perpendicular distance from the intersection point of \(p\) and \(q\) to the \(x -\)axis. Suppose by counting the grid squares, \(b = 6\) units and \(h=4\) units.

Step3: Calculate the area

Use the formula \(A=\frac{1}{2}bh\). Substitute \(b = 6\) and \(h = 4\) into the formula: \(A=\frac{1}{2}\times6\times4=12\) square units.

Answer:

a. Right - triangle. We assume we can visually identify a 90 - degree angle formed by the lines.
b. 12 square units.