Use the phrases in the word bank to complete this proof. 5. Given: PQRQ, ZPQS E ZRQS
QS QS,
CPCTC,
APQS E ARQS
Prove: PE ZR
Statements
Reasons
1. Given
1. PQ ERQ, ZPQS = ZRQS
2. a.
2. Reflexive Property of
3. b.
3. SAS
4. ZP ZR
4. c.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation:

pretty sure 750 each month!

step-by-step explanation: