what does similar but not congruent mean tho

for b does that mean if 2 triangles rest in the same line, they are mirror images and the lines of each triangle are equal?

In this case the three lengths are the same and one of the lengths is common.

The angles involved in the triangle must be the same.

This means that the inclination (gradients) of all the corresponding lines are at equal steepness.

So, the triangles must be symmetrical to a line.

We can also prove other triangles are congruent, but this is more difficult.

Remember that two similar triangles have the same shape but not the same size. So, all the corresponding angles are equal but all the corresponding sides are in fixed ratios.

We are looking for two triangles with the same shapes and angles but not the same size.

sorry i still dont really understand the symmetry one, can you explain to me again? thank you :)

I update you this later, now in class

I drew a diagram for your reference. With the angles of inclination being the same, the lines must have been at the same gradient (two lines with the same gradient will make the same angle with the horizontal axis, a property which you will learn in coordinate geometry if you have not realised it yet).

If you put your pen at an angle and rest the top of the pen against a mirror, you will notice that in the mirror image, the gradient will be the same as your pen gradient.

The pen is like your line AD and the mirror image is like your BC. They are symmetrical about the mirror.

Basically if two triangles are congruent and they are resting on the common base, then either one of the following applies.

1. The triangles overlap each other perfectly

2. The triangles are reflections of each other (since they are put the other way).

Maybe this would be easier to explain with two cut-out congruent triangles from a paper.