Math Problem Statement

Ross drew three right triangles that have the side lengths shown below.

Part A Correctly select which of Ross’s triangles lie on the same line. A.Triangle 1 B.Triangle 2 C.Triangle 3 D.None 4b. Part B Which statement is true about the selected triangles? A.The triangles are on the same line because they have similar slopes that simplify to 34 . B.The triangles are on the same line because they have congruent slopes that simplify to 43 . C.The triangles are on the same line because they have congruent slopes that simplify to 32 . D.The triangles are not on the same line because the slopes cannot be determined.

Solution

To solve this problem, we need to analyze the side lengths of the three right triangles Ross drew and then determine whether any of them lie on the same line by evaluating their slopes.

For right triangles, the slope of the line connecting two points can be calculated as the rise over run. This means the ratio of the vertical side (rise) to the horizontal side (run).

Here’s how to approach it step-by-step:

Part A

  1. Find the slope of each triangle:

    • For a right triangle, we will use the formula for the slope between two points, given by the vertical side (height) and the horizontal side (base). The slope is the ratio of the height to the base.
    • So, for each triangle, calculate the slope as: Slope=vertical sidehorizontal side\text{Slope} = \frac{\text{vertical side}}{\text{horizontal side}}
  2. Compare the slopes:

    • If two triangles share the same slope, they are on the same line.

Part B

After determining which triangles have the same slope, select the correct option from the list.

To proceed accurately, I'll need the specific side lengths of the three right triangles Ross drew. Could you provide the measurements or any additional data from the drawing?

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Math Problem Analysis

Mathematical Concepts

Analytical Geometry
Slopes of Lines
Right Triangles
Similar Triangles

Formulas

Slope formula: slope = rise/run
Similarity condition: two triangles are similar if their corresponding angles are equal and their sides are proportional

Theorems

Slope theorem
Triangle similarity theorem

Suitable Grade Level

Grades 8-10