Answer:
1. True
2.False.
3. True.
4. True.
5. True.
Step-by -step explanation:
See the diagram of triangles attached to this question.
Now,
Statement 1: Triangle ABC and triangle ADE are similar. This is true.
Since BC and DE are two vertical lines and are parallel to each other. Hence, all three angles of Δ ABC and Δ ADE are the same.
Statement 2: [tex]\frac{y}{x} = \frac{m}{2}[/tex] is false as [tex]\frac{y}{x} = m[/tex] is true.
Statement 3: The hypotenuse of the triangle ABC has the same slope as the hypotenuse of the triangle ADE. This is also a true statement.
Since, slope of AE = slope of AC and [tex]\frac{y}{x} = m[/tex] is true.
Statement 4: Slope of the line AE is m. This statement is also true.
Since, [tex]\frac{y}{x} = m[/tex] is true.
Statement 5: The equation of the line AE is y = mx. This is true.
As the line has slope = m and it passes through origin O(0,0). (Answer)
