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10 points pls help!

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 3, 0, B at ordered pair 4, negative 2, C at ordered pair 1, negative 3. A triangle A prime B prime C prime has A prime at ordered pair negative 3, 0, B prime at ordered pair negative 4, negative 2, C prime at ordered pair negative1, negative 3.

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

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

10 points pls helpTriangle ABC is transformed to triangle A B C as shown belowA coordinate grid is shown from negative 4 to 0 to 4 on both x and yaxes A triangl class=

Respuesta :

calculista

Answer:

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

Step-by-step explanation:

we know that

The transformation of the figure is a reflection, so after the transformation  the shape still has the same size, area, angles and line lengths.

the triangles ABC and A'B'C' are congruent

therefore

the corresponding sides and corresponding angles are equal

so

The relationship between the measures of the angles of the two triangles is

[tex]m<ABC=m<A'B'C'[/tex]

[tex]m<BCA=m<B'C'A'[/tex]

[tex]m<BAC=m<B'A'C'[/tex]

The given transformation that maps ΔABC to ΔA'B'C' is a reflection.

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 B prime C prime A prime (B'C'A').

Reasons:

Known parameters  

Vertex coordinates of triangle ABC are; A(3, 0), B(4, -2), and C(1, -3)

Vertex coordinates of triangle A'B'C' are; A'(-3, 0), B'(-4, -2), and C'(-1, -3)

The transformation that maps ΔABC to ΔA'B'C is therefore;

(x, y) [tex]\underrightarrow {Transformation}[/tex](-x, y)

The above transformation is the same as a reflection across the y-axis.

(x, y) [tex]\underrightarrow {r_{y-axis}}[/tex](-x, y)

Given that a reflection is a rigid transformation, we have;

ΔABC ≅ ΔA'B'C'

Therefore;

m∠ABC = m∠A'B'C'

m∠BCA = m∠B'C'A'

m∠BAC = m∠B'A'C'

Which gives;

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

Learn more here:

https://brainly.com/question/24619225

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