Question 1

Triangle TSR and triangle PQR are similar right triangles. The coordinates of all the vertices are integers. Which statement is true about the slope of $ \overline{RT}$  and the slope of $\overline{PR}$ ?

Accepted Answer

The slope of $ \overline{RT}$ is equal to the slope of $\overline{PR}$, because the ratio of change in y-values of the endpoints to the change in x-values of the endpoints is the same for  $ \overline{RT}$ and $\overline{PR}$.

Answer

The relationship between the slope of $ \overline{RT}$ and the slope of $\overline{PR}$ cannot be determined, because the triangles are congruent.

Answer

The slope of $ \overline{RT}$ is greater to the slope of $\overline{PR}$, because the ratio of change in y-values of the endpoints to the change in x-values of the endpoints is the greater  for  $ \overline{RT}$ and $\overline{PR}$.

Answer

The slope of $ \overline{RT}$ is less than to the slope of $\overline{PR}$, because the ratio of change in y-values of the endpoints to the change in x-values of the endpoints is the less for  $ \overline{RT}$ and $\overline{PR}$.

Question 2

Triangle WXY and triangle VZY are similar right triangles. The coordinate of all the vertices are integers. Which statement is true about the slope of $\overline{VY}$ and the slope of $\overline{WY}$?

Accepted Answer

The slope of $\overline{VY}$ is equal to the slope of $\overline{WY}$, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is same for $\overline{VY}$ as it is for $\overline{WY}$.

Answer

The slope of $\overline{VY}$ is less than the slope of $\overline{WY}$, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for $\overline{VY}$ as it is for $\overline{WY}$.

Answer

The slope of $\overline{VY}$ is greater than  the slope of $\overline{WY}$, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for $\overline{VY}$ as it is for $\overline{WY}$.

Answer

The relationship between the slope of $\overline{VY}$ and the slope of $\overline{WY}$ cannot be determined, because the triangles are congruent.

Question 3

Triangle PQR and triangle STU are similar right triangles. Which proportion can be used to show that the slope of $\overline{PR}$ is equal to the slope of $\overline{SU}$?

Accepted Answer

$\frac{2 - 8}{6 - (-3)}$ = $\frac{4 - 6}{3 - 0}$

Answer

$\frac{6- 3}{2- 4}$ = $\frac{0 - (-3)}{3 - 0}$

Answer

$\frac{6 - (-3)}{2 - 8}$ = $\frac{6 - 8}{4 - 6}$

Answer

$\frac{2- 4}{6- 3}$ = $\frac{3 - 0}{0 - (-3)}$

Question 4

Triangle KJL and triangle NML are similar right triangles. Which proportion can be used to show that the slope of $\overline{LK}$ is equal to slope of $\overline{NL}$?

Accepted Answer

$\frac{5 - 2}{2 - 0}$ = $\frac{2 - (-4)}{0 -(-4)}$

Answer

$\frac{2 - 0}{5 - 2}$ = $\frac{0 -(-4)}{2 - (-4)}$

Answer

$\frac{5 - (-4)}{0 - 0}$ = $\frac{2 -(-4)}{0 - 0}$

Answer

$\frac{5 - 5}{2 - 0}$ = $\frac{(-4) - (-4)}{(-4)  - 0}$

Question 5

Triangle JKL and triangle FGH are similar right triangles. Based on this information, which statement is true?

Accepted Answer

The slope of the hypotenuse of triangle JKL is equal to the slope of the hypotenuse of triangle FGH.

Answer

The slope of the hypotenuse of triangle JKL is greater than the slope of the hypotenuse of triangle FGH.

Answer

The relationship between the slope of the hypotenuse of triangle JKL  and the slope of the hypotenuse of triangle FGH cannot be determined.

Answer

The slope of the hypotenuse of triangle JKL is less than the slope of the hypotenuse of triangle FGH.

Question 6

Triangle ABC and triangle CDE are similar right triangles. Based on this information, which statement is true??

Accepted Answer

The slope of the hypotenuse of triangle ABC is equal to the slope of the hypotenuse of triangle CDE.

Answer

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

Answer

The slope of the hypotenuse of triangle ABC is greater than the slope of the hypotenuse of triangle CDE.

Answer

The slope of the hypotenuse of triangle ABC is less than the slope of the hypotenuse of triangle CDE.

Question 7

Triangle JKL and triangle MNP are similar right triangles. Which proportion can be used to show that the slope of$ \overline{JL}$ is equal to the stop of $\overline{MP}$?

Accepted Answer

$\frac{(-6)- (-3)}{(-8) - 4}$ = $\frac{(-5)- (-4)}{(-4) - 0}$

Answer

$\frac{(-5) - (-4)}{(-4)- 0}$ = $\frac{(-4) - (-3)}{0 - 4 }$

Answer

$\frac{(-8) - 4}{(-6)- (-3)}$ = $\frac{(-4) - 0}{(-5)- (-4)}$

Answer

$\frac{(-4) - (-3)}{(-8)- (-4)}$ = $\frac{(-4) - (-3)}{0 - 4 }$

Question 8

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

Accepted Answer

The slope of the hypotenuse of triangle JLP is equal to the slope of the hypotenuse of triangle MNP.

Answer

The slope of the hypotenuse of triangle JLP is less than the slope of the hypotenuse of triangle MNP.

Answer

The slope of the hypotenuse of triangle JLP is greater than the slope of the hypotenuse of triangle MNP.

Answer

The relationship between the slope of the hypotenuse of triangle JLP and the slope of the hypotenuse of triangle MNP cannot be determined.

Question 9

Triangle ABC and triangle DEF are similar right triangles. The coordinates of all the vertices are integers. Which statement is true about the slope of $\overline{AC}$ and the slope of $\overline{DF}$ ?

Accepted Answer

The slope of $\overline{AC}$ is equal to the slope of $\overline{DF}$, 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  $\overline{AC}$ as it is for $\overline{DF}$.

Answer

The slope of $\overline{AC}$ is greater than the slope of $\overline{DF}$, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the greater for  $\overline{AC}$ as it is for $\overline{DF}$.

Answer

The slope of $\overline{AC}$ is less than the slope of $\overline{DF}$, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the less for  $\overline{AC}$ as it is for $\overline{DF}$.

Answer

The relationship between the slope of $\overline{AC}$ and the slope of $\overline{DF}$ cannot be determined, because the triangles are congruent.

Question 10

Triangle ABD and triangle ECD are similar right triangles. Which proportion can be used to show that the slope of $\overline{ED}$ is equal to the slope of $\overline{AD}$?

Accepted Answer

$\frac{(-5) - 7}{4 - (-4)}$ = $\frac{1 - 7}{4 - (-4)}$

Answer

$\frac{4 - (-4)}{(-5) - 7}$ = $\frac{4 - (-4)}{1 - 7}$

Answer

$\frac{(-5) - 1}{4 - 0}$ = $\frac{(-5) - 7}{4 - 4}$

Answer

$\frac{4 - 0}{(-5) - 1}$ = $\frac{4 - 4}{(-5) - 7}$

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