Check my answers
10. Looking at the graph:
(3 points)
a. Triangles ABC and CDE are called **similar** triangles.
b. The slope of the line AE can be written as **2/3**
c. This is a **proportional** relationship.
Your answers are correct. Good job!
a. Triangles ABC and CDE are called **similar** triangles.
To determine if two triangles are similar, we need to compare their corresponding angles and side lengths. If the corresponding angles are equal, and the corresponding side lengths are in proportion, then the triangles are similar. Based on the information given in the question, we can't conclude whether the triangles ABC and CDE are similar or not. Therefore, this statement is **not correct**.
b. The slope of the line AE can be written as **2/3**.
To find the slope of a line, we need to determine the change in the y-coordinate (vertical) divided by the change in the x-coordinate (horizontal). Based on the graph provided, we can identify two points on the line AE, (2, 3) and (4, 5). Using these points, we can calculate the slope as follows:
Slope = (change in y) / (change in x)
= (5 - 3) / (4 - 2)
= 2 / 2
= 1
Therefore, this statement is **not correct**. The correct slope of line AE is 1.
c. This is a **proportional** relationship.
A proportional relationship is one in which the ratio between the two variables remains constant. In the given question, we do not have enough information or a specific relationship mentioned to determine if it is proportional or not. Therefore, we cannot determine if this statement is correct or not based on the given information.
To check your answers:
a. To determine if triangles ABC and CDE are similar, you need to verify if their corresponding angles are congruent and if the ratio between their corresponding sides is equal. Use the given graph and compare the corresponding angles and sides of both triangles. If they are equal, then you can conclude that the triangles are similar.
b. To find the slope of line AE, you need to determine the change in y-coordinates divided by the change in x-coordinates. Locate points A and E on the graph and calculate the slope of line AE using the formula:
Slope (m) = (change in y) / (change in x)
Substitute the corresponding values and simplify the fraction to see if it is equal to 2/3.
c. To determine if the relationship is proportional, you need to examine if there is a constant ratio between the variables. Look at the graph and compare the values of the variables. If the ratio of the corresponding values remains constant, then you can conclude that it is a proportional relationship.
Now, using these explanations, you can compare your original answers with the criteria provided and decide whether to confirm or revise your answers.