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Triangle ABC is transformed to triangle A′B′C′, as shown below:

A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.

Which equation shows the correct relationship between the measures of the angles of the two triangles?

The measure of angle CAB = The measure of angle C prime B prime A prime
The measure of angle BCA = The measure of angle A prime B prime C
The measure of angle CAB = The measure of angle C prime A prime B prime
The measure of angle BCA = The measure of angle C prime A prime B prime

Question

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Respuesta :

AFOKE88 AFOKE88 · Answer 1 · 2022-07-14T17:56:40+02:00

The equation that shows the correct relationship between the measures of the angles of the two triangles is;

Option D: The measure of angle BCA = The measure of angle C prime A prime B prime

We are told that Triangle ABC is transformed to triangle A′B′C′.

Now, the triangle ABC and A'B'C' are similar triangles and we know that similar triangles angles are congruent. Thus;

From the given coordinates, we can say that;

∠BAC = ∠B'A'C'

∠ABC = ∠A'B'C'

∠ACB = ∠A'C'B'

Thus, the equation that shows the correct relationship between the measures of the angles of the two triangles is;

The measure of angle BCA = The measure of angle C prime A prime B prime

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