Triangle ABC undergoes a series of transformations to result in triangle DEF.

Is triangle DEF congruent to triangle ABC ?

Is it Congruent or Not congruent?

1.)) Triangle ABC is translated 3 units up and 5 units right, and then dilated by a scale factor of 4 to form triangle DEF.
(congruent or NOT congruent)

2.)) Triangle ABC is reflected over the x-axis, and then translated 6 units down and 6 units left to form triangle DEF.
(congruent or NOT congruent)

3.)) Triangle ABC is rotated 180°, and then reflected over the line y=x to form triangle DEF.
(congruent or NOT congruent)

I personally think the first 2 are congruent, and the 3rd is not, but I am not completely sure.

Congruent means same size same shape...

Is 1) still the same SIZE when you do a dilation of scale factor 4...

I'm not sure about these, they are kind of hard for me to understand. But I think the size wouldn't stay the same.

So #1 is NOT congruent : )

#2 is correct : )

#3... the shape is changed if a dilation is done. A slide, flip or turn does not change the shape (just the orientation of the object).
So what do you think about 3?

Thanks! :)

And yes for 3, I think it's congruent. If the shape stays the same and does not change.

Excellent work : )

Thanks @MsPi_3.14159265 ! :D

I greatly appreicte your help today!! :)

To determine if two triangles are congruent, we need to examine if their corresponding sides and angles are equal in measure.

Let's analyze each scenario:

1. Translation (3 units up and 5 units right) followed by a dilation (scale factor of 4):
When a triangle undergoes a translation, its shape and size remain the same, just in a different position. Following the translation, the triangle is dilated by a scale factor of 4 which means all side lengths and angles are multiplied by 4. Since the transformation only affects position and size, the corresponding angles and side lengths of the two triangles remain equal. Therefore, triangle DEF is congruent to triangle ABC.

2. Reflection over the x-axis followed by a translation (6 units down and 6 units left):
Reflection over the x-axis involves flipping the triangle vertically, while keeping its size and shape intact. After the reflection, the triangle is translated down and left. This only affects the position and not the shape or size of the triangle. As a result, the corresponding angles and side lengths of the two triangles remain equal. Therefore, triangle DEF is congruent to triangle ABC.

3. Rotation of 180° followed by reflection over the line y=x:
A 180° rotation flips the triangle upside down, but does not change its size or shape. The triangle is then reflected over the line y=x, which involves interchanging the x and y coordinates of each vertex. This transformation changes the position and the orientation of the triangle, which affects the order of the vertices. As a result, the corresponding angles and side lengths of the two triangles are not equal. Therefore, triangle DEF is not congruent to triangle ABC.

Your understanding is correct. Triangles 1 and 2 are congruent, but triangle 3 is not congruent to triangle ABC.

I don't think it stays the same size.