Given: Quadrilateral PQRT, QSV, PTV, QV bisects RT, and QR || PV. Prove: QS=VS

What is the statements and reasons

The answer is below

Step-by-step explanation:

Two triangles are said to be congruent if all the three sides and three angles of one triangle is equal to the three sides and three angles of another triangle.

Statement                               Reason

QV bisects RT at point           Given

S and QR || PV.

RS ≅ TS                                   Definition of bisection.

∠QSR = ∠TSV                          Vertical angles are congruent to each other.

∠QRS ≅ ∠VTS                         Alternate interior angles are equal.

ΔQRS ≅ ΔVTS                        Angle-side-angle congruence theorem. If

                                                two angles and an included side of one

                                                triangle is equal to two angles and an

                                                included side of another triangle, then both

                                                triangles are congruent.

QS ≅ VS                                  Corresponding sides of congruent triangles

                                                are equal.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb