2 geometry Qs: Use a piece of graph paper to plot three points to create a triangle.

Ficle

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1. Use a piece of graph paper to plot three points to create a triangle. Name the points A, B and C. Choose a scale factor greater than 1 and draw a dilated image of the triangle. Name the corresponding vertices A', B' and C'.

1). Find the lengths of segments AB and A'B' using either the Pythagorean Theorem or the distance formula.
2). Show that the ratio of the lengths of the image and pre-image segments measured above correspond to the scale factor chosen.
3). Depending on whether or not the segments used to create the triangles pass through the center of dilation, describe the relationship between the three pairs of corresponding segments.


2. Explain why all equilateral triangles are similar. Give details about the sides and angles to support your explanation. Support your answer with an example.
 
You've posted several exercise questions in your threads without showing any efforts or asking any questions about the exercises. What have you tried or thought about?
 
1. Use a piece of graph paper to plot three points to create a triangle. Name the points A, B and C. Choose a scale factor greater than 1 and draw a dilated image of the triangle. Name the corresponding vertices A', B' and C'.

Do you understand what these words mean? A "dilated image" with "scale factor greater than 1" means a similar triangle that is larger than the original one. Since you are allowed to choose whatever "scale factor" you want, as long as it is larger than 1, take it equal to two. Now look at the coordinates of A, B, and C on your graph. You can make a "dilated" triangle, A', B', C', with "scale factor" 2, by multiplying the coordinates by 2.

1). Find the lengths of segments AB and A'B' using either the Pythagorean Theorem or the distance formula.
Do you know what the "distance formula is? If A has coordinates \(\displaystyle (x_A, y_A)\) and B has coordinates \(\displaystyle (x_B. y_B)\) then the distance between A and B is \(\displaystyle \sqrt{(x_A- x_B)^2+ (y_A- y_B)^2}\). Use the coordinates for your points to determine those two distances.

2). Show that the ratio of the lengths of the image and pre-image segments measured above correspond to the scale factor chosen.
3). Depending on whether or not the segments used to create the triangles pass through the center of dilation, describe the relationship between the three pairs of corresponding segments.
With scale factor 2, that should be fairly simple. Compare the values you got for AB and A'B'

2. Explain why all equilateral triangles are similar. Give details about the sides and angles to support your explanation. Support your answer with an example.
Okay, do you know what "equilateral triangles" are? Do you know what "similar triangles" are?
 
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