Similar Triangles on a Coordinate Plane

Triangle ABC and triangle DEF are similar right triangles.

Based on the information, which statement is true?

• The slope of the hypotenuse of triangle ABC is less than the slope of the hypotenuse of triangle DEF.

• The slope of the hypotenuse of triangle ABC is equal to the slope of the hypotenuse of triangle DEF.

• The slope of the hypotenuse of triangle ABC is greater than the slope of the hypotenuse of triangle DEF.

• The relationship between the slope of the hypotenuse of triangle ABC and the slope of the hypotenuse of triangle DEF cannot be determined.

There are similar right triangles on a coordinate plane. Triangle MAP has a hypotenuse with endpoints at (1, 0) and (3, 4). Triangle ARM has a hypotenuse with endpoints at (1, 0) and (5, 8). Which statement correctly describes the relationship between slopes of the hypotenuses?

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Triangles ABD and BCE are similar right triangles. Which proportion can be used to show that the slope AB is equal to the slope BC?

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The slope, m, of the dotted line shown below is 3. Which triangles could represent the 2 right triangles along the line?

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Triangle DEF and triangle GHI are similar triangles. Based on the information, which statement is true?

• The relationship between the slope of the hypotenuse of triangle DEF and the slope of the hypotenuse of triangle GHI cannot be determined.

• The slope of the hypotenuse of triangle DEF is greater than the slope of the hypotenuse of triangle GHI.

• The slope of the hypotenuse of triangle DEF is less than the slope of the hypotenuse of triangle GHI.

• The slope of hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI.

Triangle DEF and triangle ABC are similar triangles. Which proportion can be used to show that AC and DF have equivalent slopes?

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Two right triangles each have a hypotenuse located along a line on the coordinate grid as shown. Which of the following statements is correct?

• ∆LOQ is similar to ∆MNP, and the coordinates of their vertices can be used to find that line has a slope of 6.

• ∆LOQ is not similar to ∆MNP, but coordinates of their vertices can be used to show that the line has a slope of ⅔.

• ∆LOQ is similar to ∆MNP, and the coordinates of their vertices can be used to find that the line has a slope of 1.5.

• ∆LOQ is not similar to ∆MNP, but the coordinates of their vertices can be used to find that the line has a slope of 2.

Triangles PQR and RST are similar right triangles. Which proportion can be used to show that the slope of PR is equal to the slope of RT?

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Similar right triangles are shown on the coordinate grid. Which proportion shows the equality of the slopes of AC and AN?

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What conclusion can be reached regarding the figure?

• The simplified ratio of the vertical height to the horizontal length of both triangles is 6 to 8

• The simplified ratio of the vertical height to the horizontal length of both triangles is 12 to 9

• The simplified ratio of the vertical height to the horizontal length of both triangles is 3 to 4

• The simplified ratio of the vertical height to the horizontal length of both triangles is 4 to 3