Question

T is the midpoint of RS. Complete the proof that AQST = AQRT.

R

S

Statement

Reason

T is the midpoint of RS

Given

2

QT L RS

Given

LQTR & LQTS

RT M ST

Definition of midpoint

5

QT a QT

6

AQST % AQRT

SAS

Answer 1

The characteristics of the field diagram and the equations provided indicate that the charges on objects R and T are the same, and the charge on object S is about twice that because the field lines around S are denser and start farther away than those around R and T.

Step-by-step explanation:

The question involves physics concepts, specifically electric charges and electric fields. When describing the characteristics of a field diagram that indicates the magnitudes of the charges, one important aspect is the comparison of electric field line density and starting points around objects. The details provided suggest that the vectors (field lines) around objects R and T are about the same length and start at about the same distance from the objects, which implies that the charges on R and T are about the same. Additionally, the field lines around S start further away and at a larger density, which suggests that the charge on S is larger. The usage of the equations qr|d² = qs|D² and as| ±R=D² | d² = 36 | 16 = 2.25 indicates that the field strength related to charge S is 2.25 times that of R and T, thus suggesting that the charge on S is about twice that on R and T.

Answer 2

The proof demonstrates that ΔAQST is congruent to ΔAQRT by utilizing the Side-Angle-Side (SAS) Postulate, assuming that T is the midpoint of RS and QT is perpendicular to RS.

Step-by-step explanation:

Geometric proofs, specifically involving congruent triangles. To prove that ΔAQST is congruent to ΔAQRT, one can apply the Side-Angle-Side (SAS) Postulate.

The given information already tells us that T is the midpoint of RS, implying that RT is congruent to ST by the Definition of Midpoint. Also, it's given that QT is perpendicular to RS, meaning that ∠QTR and ∠QTS are right angles and therefore congruent. Since QT is congruent to itself by the Reflexive Property of Congruence, the triangles ΔAQST and ΔAQRT indeed have two sides and the included angle congruent, satisfying the criteria for triangle congruence by SAS.