Match the reasons to the statements in the proof.

1. m∠1 + m∠5 = 180° and m∠1 + m∠4=180°
subtraction property of equality
2. m∠1 + m∠5 = m∠1 + m∠4
substitution
3. m∠5 = m∠4
if alternate interior angles equal, then lines are ||.
4. ray yz is parallel to ray uv
given

1. and ; given

2. ; substitution

3.; subtraction property of equality

4. Ray YZ is parallel to ray UV; if alternate interior angles equal , then lines are parallel.

Step-by-step explanation:

Given

To prove that YZ is parallel to UV.

Proof:

1.Statement: and

Reason; Given

2. Statement:

Reason: By using substitution property

3.Statement:

Reason: Subtraction property of equality.

4.Statement: Ray YZ is parallel to Ray UV

Reason: If alternate interior angles equal, then lines are parallel.

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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