Answer:
Step-by-step explanation:
Alright we need to prove that both the triangles are similar so lets get started
The slope formula is:
Slope = Change in y / Change in x
m = Δy / Δx
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\[/tex]
Where, m is the slope and [tex](x_1,y_1) , (x_2,y_2)\\[/tex] are any points on the line
In this graph we are given three points which are
(0 , 2) , ( 6 , 6) and (9 , 8)
So for our first triangle we use the 2 points (0 , 2) and (6 ,6) and calculate the slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{6-2}{6-0}\\\\m=4/6\\\\m=2/3\\[/tex]
So the slope turns out to be 2/3 , Now for our second triangle use the 2 points (6 , 6) and (9 , 8)
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{8-6}{9-6}\\\\m=2/3\\[/tex]
So we can see the the slope's are equal that's the answer to your first part.
Second part
Yes they are similar due to the property of corresponding angles where angle x of the first triangle equals angle x for the second triangle and angle y for the first triangle equals angle y for the second triangle and both the triangles have 90° se they are similar because all three angles are similar. (AAA = angle angle angle property) I have attached a to make you understand it better.
