Similar Triangles and Slope
Question 1
Which statement is FALSE about the triangles shown on the graph?
Responses
A The triangles are congruent.The triangles are congruent.
B The triangles are similar.The triangles are similar.
C The triangles are proportional.The triangles are proportional.
D Both are right triangles.Both are right triangles.
Question 2
Which choice is FALSE about the slope of the line shown on the graph?
Responses
A Any two points on the line will have the same slope.Any two points on the line will have the same slope.
B The slope of the line is equivalent to cd
.The slope of the line is equivalent to c d .
C The slope of the line is equivalent to ab
.The slope of the line is equivalent to a b .
D The slope of the line is not equal to ab
or cd
.The slope of the line is not equal to a b or c d .
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The triangles are congruent (True)
The triangles are similar (True)
The triangles are proportional (True)
Both are right triangles (False) - this statement is false because there is no information provided about the angles of the triangles, so we cannot determine if they are right triangles or not.
Any two points on the line will have the same slope (True)
The slope of the line is equivalent to cd (False) - the slope of the line is given by the difference in y-coordinates divided by the difference in x-coordinates, not cd.
The slope of the line is equivalent to ab (True)
The slope of the line is not equal to ab or cd (True) - the slope of the line is not equal to either ab or cd because those are the lengths of the line segments, not the slope.
Question 1: The statement that is FALSE about the triangles shown on the graph is A - "The triangles are congruent."
Question 2: The choice that is FALSE about the slope of the line shown on the graph is C - "The slope of the line is equivalent to ab."
To determine which statement is false about the triangles shown on the graph, you need to understand the concepts of congruence, similarity, and proportionality in triangles.
A. The statement "The triangles are congruent" means that the two triangles are exactly the same in terms of shape and size. To check if the triangles are congruent, you can compare their corresponding angles and sides. If all corresponding angles are equal and all corresponding sides have the same length, then the triangles are congruent.
B. The statement "The triangles are similar" means that the two triangles have the same shape but not necessarily the same size. To check if the triangles are similar, you can compare their corresponding angles. If all corresponding angles are equal, then the triangles are similar.
C. The statement "The triangles are proportional" means that the ratios of the corresponding sides are equal. To check if the triangles are proportional, you can calculate the ratios of corresponding sides. If the ratios are equal, then the triangles are proportional.
D. The statement "Both are right triangles" means that both triangles have a right angle (an angle measuring exactly 90 degrees). To check if the triangles are right triangles, you can analyze the angles in each triangle. If one angle measures 90 degrees in each triangle, then both triangles are right triangles.
Now, analyze each statement and determine which one is false based on the definitions and criteria given above.
To determine which choice is false about the slope of the line shown on the graph, you need to understand the concept of slope and its properties.
A. The statement "Any two points on the line will have the same slope" is true. The slope of a line is a measure of the steepness of the line and is constant for any two points on the line.
B. The statement "The slope of the line is equivalent to c d" is not correct. The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates (rise over run). It is not equivalent to the quotient of c and d.
C. The statement "The slope of the line is equivalent to a b" is also not correct. The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates, not by the ratio of a and b.
D. The statement "The slope of the line is not equal to ab or cd" is correct. The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates, not by the product or division of ab or cd.
Based on the definitions and properties of slope, the false statement about the slope of the line shown on the graph is either B or C.