Given: R is the midpoint of QT , QS=TS Prove: RQS = RTS

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The answer is below

Step-by-step explanation:

Prove ∠RQS = ∠RTS

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

QS ≅ TS                               Given

RS ≅ RS                               Reflexive property of congruence.      

R is the midpoint of QT       Given

QR = RT                                R is the midpoint of QT. Therefore by

                                             definition, QR = RT.

ΔRQS = ΔRTS                       Side-side-side triangle congruence theorem. If

                                             three sides of one triangle is equal to three

                                             sides of another triangle, then both triangles

                                             are congruent to each other.

∠RQS = ∠RTS                        Corresponding angles of congruent triangles

                                              are equal.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions