27.05.2023

Wrote a two column proof
Given: ABCS is a parallelogram
Prove: E is midpoint of AC

. 4

Faq

Mathematics
Step-by-step answer
P Answered by Specialist

C

Step-by-step explanation:

Median of triangle: It is a line segment joining a vertex to the midpoint of the opposite side.

Consider ΔABC, point F id the midpoint of line segment AB and E is the midpoint of luine segment AC.

Draw line segments FC and BE(medians of  triangle). G is the point where line segment FC and BE meet. Now, Join AG.

Let H be the point outside the ΔABC and AG passs through the point H  such that AG intersects BC at D. BH and HC are dashed lines.

We need to show that D is the midpoint of BC. The correct logical order for proof will be:

III. GC is parallel to line segment BH and line segment BG is parallel to line segment HC.

IV.  Line segment FG is parallel to line segment BH and line segment GE is parallel to line segment HC.

I. BGCH is a parallelogram as opposite sides are parallel (from III.)

II. Since, diagnols of a parallelogram bisect each other. Henc, we get BD=DC.

Therefore, D is mid pont of BC.

It implies that AD is also a median.

Hence, all the three medians that are: BE,FC and AD passes through a common vertex G.


Will mark brainliest.!  use δabc to answer the question that follows:  triangle abc. point f lies on
Mathematics
Step-by-step answer
P Answered by PhD

II establishes the lines are parallel, then III renames the parallel lines to refer to specific segments. The order of these statements should be II, III.

IV establishes that BGCH is a parallelogram, then I makes use of the properties of a parallelogram. The order of these statements should be IV, I.

The appropriate choice is ...

... II, III, IV, I . . . . . . . the 3rd selection

Mathematics
Step-by-step answer
P Answered by PhD
Given: ΔABC

When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point are as follows:

Statements                                                          Justifications

Point F is a midpoint of Line segment AB        by Construction               
Point E is a midpoint of Line segment AC
Draw Line segment BE
Draw Line segment FC 

Point G is the point of intersection between
Line segment BE and Line segment FC               Intersecting Lines Postulate

Draw Line segment AG                                        by Construction

Point D is the point of intersection between
Line segment AG and Line segment BC              Intersecting Lines Postulate

Point H lies on Line segment AG such that
Line segment AG ≅ Line segment GH                 by Construction

Line segment FG is parallel to line segment
BH and Line segment GE is parallel to line
segment HC                                                        Midsegment Theorem

Line segment GC is parallel to line segment
BH and Line segment BG is parallel to
line segment HC                                                 Substitution

BGCH is a                                                        Properties of a Parallelogram parallelogram                                                   (opposite sides are parallel)

Line segment BD ≅ Line segment                    Properties of a Parallelogram DC                                                                    (diagonals bisect each other)   

Line segment AD is a median                          Definition of a Median

Thus the most logical order of statements and justifications is: II, III, IV, I
Mathematics
Step-by-step answer
P Answered by PhD

Let's try to render the first part of the proof a bit more legibly.


Point F is a midpoint of Line segment AB

Point E is a midpoint of Line segment AC

Draw Line segment BE

Draw Line segment FCby Construction

Point G is the point of intersection between Line segment BE and Line segment FCIntersecting Lines Postulate

Draw Line segment AGby Construction

Point D is the point of intersection between Line segment AG and Line segment BCIntersecting Lines Postulate

Point H lies on Line segment AG such that Line segment AG ≅ Line segment GHby Construction


OK, now we continue. We need to prove some parallel lines; statement 4 lets us do so.


IVLine segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC Midsegment Theorem


Now that we've shown some segments parallel we extend that to collinear segments.


IIILine segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC Substitution


We have enough parallel lines to prove a parallelogram


IBGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel)


Now we draw conclusions from that.


IILine segment BD ≅ Line segment DC Properties of a Parallelogram (diagonals bisect each other)


IV III I II, second choice

Mathematics
Step-by-step answer
P Answered by PhD

  B:  II, IV, I, III

Step-by-step explanation:

We believe the proof statement — reason pairs need to be ordered as shown below

  Point F is a midpoint of Line segment AB Point E is a midpoint of Line segment AC — given

  Draw Line segment BE Draw Line segment FC — by Construction

  Point G is the point of intersection between Line segment BE and Line segment FC — Intersecting Lines Postulate

  Draw Line segment AG — by Construction

  Point D is the point of intersection between Line segment AG and Line segment BC — Intersecting Lines Postulate

  Point H lies on Line segment AG such that Line segment AG ≅ Line segment GH — by Construction

__

  II Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC — Midsegment Theorem

  IV Line segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC — Substitution

  I BGCH is a parallelogram — Properties of a Parallelogram (opposite sides are parallel)

  III Line segment BD ≅ Line segment DC — Properties of a Parallelogram (diagonals bisect each other)

__

  Line segment AD is a median Definition of a Median


Fast use δabc to answer the question that follows:  triangle abc. point f lies on ab. point d lies o
Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

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