Triangle LKJ is similar to triangle TSR. Which of the following statements is true?
A.
The slope of KJ is equal to the slope of TS.
B.
The slope of JL is equal to the slope of RT.
C.
The slope of JL is equal to the slope of SR.
D.
The slope of KJ is equal to the slope of RT.
C. The slope of JL is equal to the slope of SR.
nope: try B
Apologies for the mistake. You are right.
B. The slope of JL is equal to the slope of RT.
To determine which statement is true, we need to understand the concept of similar triangles and how it relates to the slopes of their sides.
Similar triangles are triangles that have the same shape but possibly different sizes. In other words, the corresponding angles of similar triangles are equal, and the corresponding sides are proportional.
When two triangles are similar, we can conclude that their corresponding sides are in proportion and have equal slopes. Therefore, the statement that is true can be determined by comparing the corresponding sides of the two triangles.
In the given options:
A. The statement compares the slope of side KJ with the slope of TS. These two sides are not corresponding sides in the two triangles, so we cannot conclude that their slopes are equal. Therefore, option A is not true.
B. The statement compares the slope of side JL with the slope of RT. These two sides are corresponding sides in the two triangles since they connect the same vertices. So, if the triangles are similar, we can conclude that the slopes of JL and RT are equal. Therefore, option B may be true.
C. The statement compares the slope of side JL with the slope of SR. These two sides are not corresponding sides in the two triangles, so we cannot conclude that their slopes are equal. Therefore, option C is not true.
D. The statement compares the slope of side KJ with the slope of RT. These two sides are corresponding sides in the two triangles since they connect the same vertices. So, if the triangles are similar, we can conclude that the slopes of KJ and RT are equal. Therefore, option D may be true.
Based on the explanation, the correct answer is either option B or option D, depending on whether the slopes of JL and RT or the slopes of KJ and RT are equal. To determine which one is true, further analysis of the triangle LKJ and TSR is required, such as comparing the corresponding side lengths or angles.