Two Triangles On the graph, two right triangles have the line as the hypotenuse. In this task, you will use these triangles to show that the slope between points E and A is the same as the slope between points A and C.

Part A
Which angles of the triangles measure 90°?

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Part B
To show that the other two angle measurements in each triangle are equal, you can use parallel lines cut by a transversal. Which two pairs of line segments formed by triangle sides are parallel, and what is the transversal for each pair?

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Part C
Which angle has the same measurement as angle DEA, and how do you know that the measurement is the same?

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Part D
Which angle has the same measurement as angle DAE and why (vertical, corresponding, alternate interior, or alternate exterior angles)?

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Part E
Are the two triangles congruent? Why or why not?

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Part F
Are the two triangles similar? Why or why not?

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Part G
Write a fraction setting the vertical length of the larger triangle over its horizontal length. What does this fraction represent?

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Part H
Write a fraction setting the vertical length of the smaller triangle over its horizontal length. What does this fraction represent?

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Part I
To see if the slopes are the same, write an equation setting the two fractions equal to each other. Is this equation true? Why or why not? What does that mean about the slope between points E and A and the slope between the points A and C?

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