Lesha wants to prove that the measures of the 3 angles in a triangle always have a sum of 180°. She decided to prove this conjecture using rigid motion. She began with triangle ABC shown in Figure 1.
Which statement best describes the rigid motion she used in Figure 2 to support her proof?
A. Reflect triangle ABC across AB and across AC.
B. Rotate triangle ABC 180° about the midpoint of AB and about the midpoint of AC.
C. Translate triangle ABC along directed line segment AD and along directed line segment AE.
D. Reflect triangle ABC across AB and then translate the image along directed line segment DE.

Rigid motion involves the movement of the shape, where the size of the shape is not altered.

The statement to support her proof is:

A. Reflect triangle ABC across AB and across AC.

I've added an attachment of figures 1 and 2.

Figure 1 is the original figure before the triangle is transformed

However, in figure (2);

After the reflections, angles A, B and C lie on the straight line.

So:

--- theorem of angle on a straight line

Hence, the statement to support Iesha's proof is (a).

Read more about reflections at:

link

A

Step-by-step explanation:

Reflecting it across the lines will bring the triangle on to the other triangles. This will show that when the triangle goes under a transformation such as reflection, the angles will stay the same.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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