Question

slope and similar triangles

1. which of the following is a true statement 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 triangles.
the slopes of the two triangles are the same.

1. catherine used the two points and the right triangle shown to find the slope of the line. catherine found the slope to be \\(\frac{1}{10}\\). is she correct? explain.
2. could these two triangles below lie on the same line?
3. explain whether or not the triangles shown could lie on the same line.

#5-10: identify which line from the graph the following right triangles could lie on.

Explanation:

Step1: Solve Q1: Slope comparison

Slope = $\frac{\text{rise}}{\text{run}}$. For triangles on the same line, slopes are equal.

Step2: Solve Q2: Calculate correct slope

Points: $(4,40)$ and $(6,70)$. Slope = $\frac{70-40}{6-4}=\frac{30}{2}=15$. Catherine's $\frac{1}{10}$ is wrong.

Step3: Solve Q3: Compare triangle slopes

Slope 1: $\frac{18}{10}=1.8$, Slope 2: $\frac{2}{3}\approx0.67$. Slopes not equal, so no.

Step4: Solve Q4: Compare triangle slopes

Slope 1: $\frac{72}{12}=6$, Slope 2: $\frac{144}{24}=6$. Slopes equal, so yes.

Step5: Solve Q5: Find triangle slope

Slope = $\frac{90}{120}=\frac{3}{4}$. Match Line C (slope $\frac{6}{8}=\frac{3}{4}$).

Step6: Solve Q6: Find triangle slope

Slope = $\frac{30}{10}=3$. Match Line A (slope $\frac{9}{3}=3$).

Step7: Solve Q7: Find triangle slope

Slope = $\frac{18}{24}=\frac{3}{4}$. Match Line C (slope $\frac{6}{8}=\frac{3}{4}$).

Step8: Solve Q8: Find triangle slope

Slope = $\frac{21}{14}=\frac{3}{2}$. Match Line B (slope $\frac{9}{6}=\frac{3}{2}$).

Step9: Solve Q9: Find triangle slope

Slope = $\frac{36}{24}=\frac{3}{2}$. Match Line B (slope $\frac{9}{6}=\frac{3}{2}$).

Step10: Solve Q10: Find triangle slope

Slope = $\frac{48}{16}=3$. Match Line A (slope $\frac{9}{3}=3$).

Answer:

1. The slopes of the two triangles are the same.
2. No. The correct slope is $\frac{70-40}{6-4}=15$, not $\frac{1}{10}$.
3. No
4. Yes, because both triangles have a slope of 6.
5. LINE C
6. LINE A
7. LINE C
8. LINE B
9. LINE B
10. LINE A