Quiz about Similar Triangle Proportions Slope

Question 1

Triangle ABC and triangle EBD are similar right triangles. The coordinates of all vertices are integers. Which statement is true about the slope of BC and the slope of CD?

Accepted Answer

The slope of BC is the same as the slope of CD

Answer

The slope cannot be determined

Answer

The slope of BC is greater than the slope of CD

Answer

The slope of BC is less than the slope of CD

Question 2

The two right triangles shown below are similar. Which configuration DOES represent how triangles A and B can be placed on a coordinate plane so that the line containing the side opposite the right angle of each triangle represents the same slope?

Accepted Answer

Option A is correct

Accepted Answer

Option C is correct

Accepted Answer

Option D is correct

Answer

B.

Question 3

Which proportions DO NOT show the equality of the slopes of AC and AN? Select ALL that apply

Accepted Answer

$$\frac{-5-\left(-3\right)}{-7-\left(-8\right)}=\frac{-7-\left(-8\right)}{-1-7}$$

Accepted Answer

$$\frac{-3-\left(-8\right)}{-5-\left(-7\right)}=\frac{-8-7}{-7-\left(-1\right)}$$

Accepted Answer

$$\frac{-5-3}{-7-8}=\frac{-7-8}{-1-\left(-7\right)}$$

Answer

$$\frac{-5-\left(-7\right)}{-3-\left(-8\right)}=\frac{-7-\left(-1\right)}{-8-7}$$

Question 4

Question 4.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 5

Question 5.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 6

Triangles ABC and DEF are similar. The slope of the hypotenuse of ABC is...

Accepted Answer

The same as the hypotenuse of triangle DEF

Answer

3/4 the slope of hypotenuse of triangle DEF

Answer

4/3 the slope of hypotenuse of triangle DEF

Question 7

Triangles ABC and DEF are similar. The slope of triangle ABC is...

Accepted Answer

EQUAL TO the slope of triangle DEF.

Answer

LESS THAN the slope of triangle DEF.

Answer

GREATER THAN the slope of triangle DEF.

Question 8

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

Question 9.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 10

Question 10.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 11

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.

Accepted Answer

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.

Answer

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.

Answer

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.

Answer

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

Question 12

When given two similar triangles on the same line, they will ALWAYS have the same _______________?

Accepted Answer

slope

Answer

y-intercept

Answer

x

Answer

y

Question 13

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

Accepted Answer

The slopes of the two triangles are the same.

Answer

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

Answer

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

Answer

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

Question 14

Explain whether or not the triangles shown could lie on the same line.

Accepted Answer

Yes, because their slopes both simplify to -6.

Answer

Yes, because their slopes both simplify to 1/6.

Answer

No, because -72/12 is not the same as -144/24

Question 15

Identify the slope of the hypotenuse of triangle DEF.

Accepted Answer

1

Answer

-1

Answer

3

Answer

-3

Question 16

Which proportion can be used to show that the slope of EF is equal to the slope of BC?

Accepted Answer

$$\frac{-6-\left(-3\right)}{-6-\left(-3\right)}=\frac{-1-3}{-1-3}$$

Answer

$$\frac{-6-3}{-6-\left(-3\right)}=\frac{-1-\left(-3\right)}{-1-3}$$

Answer

$$\frac{6-3}{6-3}=\frac{1-3}{1-3}$$

Answer

$$\frac{-1-3}{-6-\left(-3\right)}=\frac{6-3}{-1-\left(-3\right)}$$

Question 17

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 18

Which proportion shows the equality of the slopes of AC and DF?

Accepted Answer

$$\frac{-4-4}{3-\left(-1\right)}=\frac{-2\ -\ 0}{2\ -\ 1}$$

Answer

$$\frac{0-1}{-2-2}=\frac{1-\left(-4\right)}{-4-3}$$

Answer

$$\frac{3-\left(-4\right)}{-4-1}=\frac{2-1}{-2-0}$$

Answer

$$\frac{-4-1}{-4-3}=\frac{-2-0}{1-2}$$

Question 19

Triangle ABC and triangle DEF...

Accepted Answer

are on the same line,

so they have the same slope.

Answer

are different sizes,

so their slopes are different.

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