Proving Right Triangles Using Slope

Which of the following is true about the triangles shown on the graph?

• The slope of the smaller triangle is smaller than the slope of the larger triangle.

• The slope of the larger triangle is larger than the slope of the smaller triangle.

• The triangles are congruent.

• The slopes of the two triangles are the same.

• The slope of line XZ is the negative reciprocal of the slope of line CA because the triangles are flipped.

• The slope of line XZ is the same as the slope of line CA because the ratios of the corresponding sides of the triangles are equivalent.

• The is no relationship between the slope of line XZ and the slope of line CA.

Which proportion could be used to show the slope of line VX is equal to the slope of line XZ?

Triangle HJK and triangle PMK are similar right triangles. The coordinates of all the verticces are integers. Which statement is true about the slope of line HK and the slope of line PK.

• The slope of line HK is less than the slope of line PK because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for line HK than it is for line PK.

• The slope of line HK is equal to the slope of line PK because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for line HK as it is for line PK.

• The slope of line HK is greater than the slope of line PK because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for line HK than it is for line PK.

• The relationship between the slope of line HK and the slope of line PK cannot be determined because the traingles are congruent.

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

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

• The relationship between the slope of the hypotenuse of triangle DEF and the slope of the hupotenuse 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 the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI.

Which of the following is true about the triangles shown on the graph?

• The slope of the smaller triangle is smaller than the slope of the larger triangle.

• The slope of the larger triangle is larger than the slope of the smaller triangle.

• The triangles are congruent. Congruent: same size, same shape.

• The slopes of the two triangles are the same.

Are the triangles drawn along the line similar? Remember: Similar: same shape, different size.

• yes

• no