Question

If two triangles are congruent which of the following statements must be true? CHECK ALL THAT APPLY

A. The triangles have the same size but not the same shape.
B. The triangles have the same size and shape
C. The corresponding sides of the triangles are congruent.
D. The corresponding angles of the triangles are congruent.

Answer 1

Definition of Congruent Triangles

If two triangles are congruent then:
1. Every angle of the first triangle is congruent to a corresponding angle of the second triangle.
2. Every side of the first triangle is congruent to a corresponding side of the second triangle.

Answer 2

Based on the definition, can you try to answer the question?

Answer 3

No i cannot

Answer 4

What does it mean for two triangles to have the same shape?

Answer 5

they are congruent

Answer 6

No.
I'll explain.

Answer 7

Look at the two triangles in the figure above.
Let's say that if you were to amplify the size of the left one, you could make it the size of the right one. Then you'd place the amplified left one on top of the right one, and it is exactly the same. That means the original small left triangle and the original large right trianlge are the same shape. Obviously, they are not the same size.

Answer 8

For example, in this sense, all squares are the same shape.
If you are given two squares of different sizes, by increasing the smaller one or decreasing the larger one, they can be made to perfectly be superimposed on one another.
Once again, that means the same shape, but not the same size.