Below is a two-column proof incorrectly proving that the three angles of δpqr sum to 180°: statements reasons draw line zy parallel to segment pq construction m∠zrp + m∠prq + m∠qry = m∠zry angle addition postulate ∠zrp ≅ ∠rpq alternate interior angles theorem ∠qry ≅ ∠pqr alternate interior angles theorem m∠rpq + m∠prq + m∠pqr = m∠zry substitution m∠zry = 180° definition of a straight angle m∠rpq + m∠prq + m∠pqr = 180° additive property of equality which statement will accurately correct the two-column proof?

Proof with statement is below.

Step-by-step explanation:

To Prove:

m∠RPQ + m∠PRQ + m∠PQR = 180°

Proof:

Draw line ZY parallel to segment PQ ............{Construction}

1. m∠ZRP + m∠PRQ + m∠QRY = m∠ZRY  .....{Angle Addition Postulate}

2. ∠ZRP ≅ ∠RPQ   ........{Alternate angles equal as ZY || PQ}

3. ∠QRY ≅ ∠PQR  .........{Alternate angles equal as ZY || PQ}

4. m∠RPQ + m∠PRQ + m∠PQR = m∠ZRY  ....{The three angles of ΔPQR equal 180° according to Substitution }

5. m∠ZRY = 180°   ......{Definition of a Straight Angle}

6. m∠RPQ + m∠PRQ + m∠PQR = 180° ...{Additive Property of Equality}...............PROVED

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕