Question

which way did it go?
you see three versions of the same triangle on a grid-but somethings different about each one.
questions:

1. how do you think triangle a turned into triangle b? what about c and d?
2. what do you notice about the size and shape of each triangle compared to the original?

Explanation:

Step1: Analyze Triangle A to B

Triangle A is reflected over the y - axis. The x - coordinates of its vertices change sign while the y - coordinates remain the same. For example, if a vertex of A is \((x,y)\), the corresponding vertex of B is \((-x,y)\).

Step2: Analyze Triangle A to C

Triangle A is rotated \(180^{\circ}\) about the origin. The x and y coordinates of its vertices change sign. If a vertex of A is \((x,y)\), the corresponding vertex of C is \((-x,-y)\).

Step3: Analyze Triangle A to D

Triangle A is reflected over the x - axis. The y - coordinates of its vertices change sign while the x - coordinates remain the same. If a vertex of A is \((x,y)\), the corresponding vertex of D is \((x,-y)\).

Step4: Analyze Size and Shape

All triangles (A, B, C, D) are congruent. Congruent triangles have the same shape (same angles) and same size (same side lengths). Transformations like reflection, rotation do not change the size and shape of a figure.

Answer:

1. Triangle A to B: reflection over the y - axis. Triangle A to C: rotation of \(180^{\circ}\) about the origin. Triangle A to D: reflection over the x - axis.
2. All triangles (A, B, C, D) are congruent (same shape and size).