Given: ABCD is a parallelogram with diagonals AC and BD intersecting at M. Prove: Segment DB and Segment AC bisect each other.

Please complete the proof by providing the reasons for each statement ABCD is a parallelogram with diagonals AC and BD intersecting at M.
Segment AB||Segment CD,
Segment BC||Segment AD
Segment AD ≅ Segment CB, Segment AB ≅ DC
∠DBA and∠BDC are alternate interior angles
∠DBA≅∠BDC
∠CMD and∠AMB are vertical angles
∠CMD ≅ ∠AMB
ΔCMD ≅ ΔAMB
Segment AM ≅ Segment MC
M is the midpoint of Segment AC

c is the final answer! : )

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: