Given: δabc
prove: the sum of the interior angle measures of δabc is 180°.

statement

reason

1. let points a, b, and c form a
triangle.

given

2. let be a line passing
through b, parallel to ,
with angles as labeled.

defining a parallel line and labeling angles

3.

4. m∠1 = m∠4, and
m∠3 = m∠5.

congruent angles have equal measures.

5. m∠4 + m∠2 + m∠5 = 180°

angle addition and definition of a straight angle

6. m∠1 + m∠2 + m∠3 = 180°

substitution

what is the missing step in this proof?

a.
statement: ∠4 ≅ ∠5, and ∠1 ≅ ∠3.
reason: alternate interior angles theorem

b.
statement: is parallel to .

reason: is a transversal cutting and .

c.
statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.

reason: alternate interior angles theorem

d.
statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.
reason: ∠1 and ∠4, and ∠3 and ∠5 are pairs of supplementary angles.

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

a 360 degree rotation

step-by-step explanation: