Question

'The following graph shows the preimage, A.ABC . You can rotate A.ABC' clockwise to get 4.A' B'C" . Finally; you can translate A4' B'C"' down to become AA" B"C" 2019 StrongMind. Created using GeoGebra 1. AABC was transformed using two rigid transformations_ Compare all of the corresponding parts (angles and sides) of the image and preimage. Describe the results_ b. Explain why the results are true: When two triangles are congruent to each other, each triangle has six parts (three angles and three sides) that are congruent to those six parts of the other triangle. This can be proven using rigid transformations. But suppose you don't know the rigid transformations that map one triangle to another_ How canyou prove the two triangles are congruent without using rigid transformations? Will you need to show that all of the parts of one triangle are congruent to all of the parts of the other triangle to prove they are congruent? Explain_ Note: Be sure to number your responses for each question; like this: 1a, Ib, Za, 2b_'

Answer 1

When you move a shape via rigid transformations, the dimensions of the shape do not change.

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

You can rotate A.ABC' clockwise to get 4.A' B'C" . Finally  you can translate A4' B'C"' down to become AA" B"C" 2019 StrongMind.

When two triangles are congruent to each other, each triangle has six parts (three angles and three sides) that are congruent to those six parts of the other triangle.

When you move a shape via rigid transformations, the dimensions of the shape do not change.

This includes translation and rotation. Since the size or measure of any of the side lengths or angles is not changing when you move the shape,

the only way that you can match one shape onto another with rigid transformations is if all of the corresponding sides and angles are congruent.

Learn more about triangles;

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