# Given: SV || TU and SVX = UTX

Step-by-step clarification: Given : ΔSVX ≅ ΔUTX SV║TU To Show : VUTS is a parallelogram Resolution:        Statements                                 Causes 1). ΔSVX ≅ ΔUTX                         5). Given 2). SV║TU                                    6). Given 3). SV = TU                                   7). ΔSVX ≅ ΔUTX     SX = UX     VX = TX                                   4). VUTS is a parallelogram        8). Definition of a parallelogram. (Definition of a parallelogram: “If reverse sides of a quadrilateral are equal and parallel and diagonals bisect one another, quadrilateral is claimed to be a parallelogram”)

its a parallelogram as a result of it has 4 sides which can be parallel to the other aspect of one another

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2 is a given which is (SV | | TU) I need assistance with the others. Step-by-step clarification:

Step-by-step clarification: WE have to finish the 2 column proof GIven that Triangle SVX=UTX and SV||TU 2) SV||TU                                    Given 3) Angle USV = angle SUT        Alternate angles for parallel strains property 3a) SV=TU                                  Congruence property for triangles 4) VUTS is a parallelogram       A pair of reverse aspect is parallel and equal Thus we discover that since SV is the same as TU and likewise parallel to TU, by property of parallelograms that the quadrilateral VUTS is a parallelogram

UVTS is a parallelogram.
A definition and a theorem can be utilized as a cause in a two-column proof.
Parallelogram is a sort of quadrilateral wherein reverse sides are equal and parallel.
Given:
Clarification:
Full two column proof.
The primary assertion is is given.
The second assertion might be and it’s given.
The third assertion might be and the reason being that the corresponding components of congruent triangles are equal.
The assertion 4 is VUTS is a parallelogram and the reason being {that a} pair of reverse sides is equal.
and implies that the other sides are equal and parallel. Due to this fact, UVTS is a parallelogram.
UVTS is a parallelogram.
Be taught extra:
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Topic: Arithmetic
Chapter:Triangles
Key phrases: triangle, two column proof, congruent, congruent triangles, parallelogram, UVTS, alternate angles, equal sides, equal angles, given, line, SV, TU, SVX, UTX, reverse sides are equal, reverse sides are parallel.

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Therefore it’s proved that VUTS is a parallelogram. Step-by-step clarification: Since ΔSVX ≅ΔUTX AND SV║TU In the same triangles ΔSVX and ΔUTX⇒ ∠TVS =∠UTV and ∠VSU =∠SUT as they’re alternate angles subsequently ∠VXS=∠UXT. Since all angles of those triangles are similar then sides of those triangles might be of similar size.Due to this fact SV=TU. Equally in triangles ΔUXV and ΔSXT ∠VSU=∠SUT (alternate angles) then ∠UST=∠SUV (remaining angles of ∠VST and ∠TUV). And ∠SVT = ∠UTV then ∠TVU=∠VTS (remaining angles of ∠SVU and ∠UTS) Since these angles are alternate angles subsequently VU║ST. And we all know all angles of ΔUVX are equal to angles of ΔSXT Due to this fact sides of those triangles might be equal VU= ST. Now we are able to say that sides ST and VU are parallel and equal. Since all reverse sides of VSTU are equal and parallel to one another subsequently VSTU is a parallelogram.