Developing Slope with Similar Right Triangles 8.4A

Triangles QUS and RTS are graphed as shown. Which of the following best describes the slope of line QS?

• The slope is 14 because the ratio of the vertical height to the horizontal length for triangle QUS is $\frac{14}{14}$ .

• The slope is -1 because the ratio of the vertical height to the horizontal length simplifies to -1 for both triangle QUS and triangle RTS.

• The slope is -1 because the ratio of the horizontal length to the vertical height simplifies to 1 for both triangle QUS and triangle RTS.

• The slope is -5 because the ratio of the horizontal length to the vertical height for triangle RTS is $-\frac{5}{5}$ .

The slope of line CA is  $-\frac{3}{2}$  . Which of the following is true about the slope of line XZ?

• 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 one-half the slope of line CA because the ratio of corresponding sides between the triangles is  $\frac{1}{2}$  .

• 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.

Tags

CCSS.HSG.GPE.B.5

CCSS.HSG.SRT.A.2

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

• $\frac{1-5}{1-2}=\frac{5-1}{3-1}$

• $\frac{1-\left(-5\right)}{1-\left(-2\right)}=\frac{5-1}{3-1}$

• $\frac{-2-\left(-5\right)}{-2-1}=\frac{5-1}{3-1}$

• $\frac{1-\left(-2\right)}{1-\left(-5\right)}=\frac{3-1}{5-1}$

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.

Tags

CCSS.HSG.GPE.B.4

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

CCSS.HSG.SRT.B.5

CCSS.HSG.SRT.C.6

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?

• $\frac{3-7}{-4-\left(-7\right)}=\frac{-5-3}{2-\left(-4\right)}$

• $\frac{3-\left(-4\right)}{7-\left(-7\right)}=\frac{-5-2}{3-\left(-4\right)}$

• $\frac{-4-\left(-7\right)}{3-7}=\frac{2-\left(-4\right)}{-5-3}$

• $\frac{-4-\left(-3\right)}{-7-7}=\frac{2-\left(-5\right)}{-4-3}$

Tags

CCSS.HSG.GPE.B.4

CCSS.HSG.GPE.B.5

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.C.6

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.

Tags

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

CCSS.HSG.SRT.B.5

Malika and Brynn both use triangles to determine the slope of the line. Malika determines the slope of the line to be -2. Brynn says the slope of the line is  $\frac{1}{2}$  . Who is correct?  Justify your answer.

Evaluate responses using AI:

OFF

The slope of a line is 3. Which of the following is a possible ratio of the vertical height of the right triangle to the horizontal length of the right triangle?

• $\frac{3}{3}$

• $\frac{4}{12}$

• $\frac{12}{4}$

• $\frac{6}{3}$