Triangle ABC and triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CE?
Responses
A 3−5−4−0
= 3−20−2
3 − 5 − 4 − 0 = 3 − 2 0 − 2
B 3−5−4−0
= 3−22−0
3 − 5 − 4 − 0 = 3 − 2 2 − 0
C 5−3−4−0
= 3−20−2
5 − 3 − 4 − 0 = 3 − 2 0 − 2
D 5−3−4−0
= 2−30−2
5 − 3 − 4 − 0 = 2 − 3 0 − 2
C 5−3−4−0
= 3−20−2
5 − 3 − 4 − 0 = 3 − 2 0 − 2
The proportion that can be used to show that the slope of AC is equal to the slope of CE is Option C: 5−3−4−0 = 3−20−2, which simplifies to 5/3 = 3/2.
To determine the proportion that can be used to show that the slope of AC is equal to the slope of CE, we need to understand the relationship between similar triangles and their slopes.
In similar triangles, corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides in one triangle is equal to the ratio of the lengths of corresponding sides in the other triangle.
Let's look at the similar right triangles ABC and CDE. We want to find a proportion that relates the slopes of AC and CE.
The slope of a line can be found using the formula: slope = (change in y-coordinate) / (change in x-coordinate).
In triangle ABC, the slope of AC can be determined by taking the difference in y-coordinates (change in y) between points A and C, and dividing it by the difference in x-coordinates (change in x) between points A and C.
Similarly, in triangle CDE, the slope of CE can be found by taking the difference in y-coordinates (change in y) between points C and E, and dividing it by the difference in x-coordinates (change in x) between points C and E.
To find the proportion that relates the slopes of AC and CE, we need to set up a ratio of these changes in y-coordinates to the changes in x-coordinates for the corresponding sides of both triangles.
Considering the responses given:
A. 3-5-4-0 = 3-20-2 : This is not the correct proportion to compare the slopes of AC and CE.
B. 3-5-4-0 = 3-22-0: This is not the correct proportion to compare the slopes of AC and CE.
C. 5-3-4-0 = 3-20-2: This is not the correct proportion to compare the slopes of AC and CE.
D. 5-3-4-0 = 2-30-2: This is the correct proportion to compare the slopes of AC and CE.
Therefore, the correct proportion that can be used to show that the slope of AC is equal to the slope of CE is 5-3-4-0 = 2-30-2.