Regents Exam Questions G.G.42: Midsegments
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G.G.42: Midsegments: Investigate, justify, and apply theorems about geometric
relationships, based on properties of the segment joining the midpoints of two sides
of the triangle
1 If the midpoints of the sides of a triangle are connected, the area of the triangle formed is
what part of the area of the original triangle?
1)
2)
3)
4)
2 In the diagram below, the vertices of
triangle ABC, and the perimeter of
What is the length, in centimeters, of
1) 6
2) 12
3) 18
4) 4
are the midpoints of the sides of equilateral
is 36 cm.
?
Regents Exam Questions G.G.42: Midsegments
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3 In isosceles triangle RST shown below,
respectively, and
is drawn. If
and state the length of
.
4 In the diagram below of
,
. Find the perimeter of
, M and N are midpoints of
and
,
and the perimeter of
is 25, determine
is a midsegment of
.
5 In the diagram of
below,
,
, and
triangle formed by connecting the midpoints of the sides of
,
,
, and
. Find the perimeter of the
.
Regents Exam Questions G.G.42: Midsegments
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6 In the diagram below of
is the midpoint of .
If
1)
2)
3)
4)
,
, and
, D is the midpoint of
, O is the midpoint of
, what is the perimeter of parallelogram CDOG?
21
25
32
40
7 In the diagram of
shown below, D is the midpoint of
and F is the midpoint of
.
If
1)
2)
3)
4)
, and G
,
24
36
40
44
, and
, E is the midpoint of
, what is the perimeter of trapezoid ABEF?
,
Regents Exam Questions G.G.42: Midsegments
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8 In
shown below, L is the midpoint of
midpoint of
.
If
1)
2)
3)
4)
,
, and
, and N is the
, the perimeter of trapezoid BMNC is
35
31
28
26
9 In
shown below, L is the midpoint of
midpoint of
.
If
1)
2)
3)
4)
, M is the midpoint of
,
26
28
30
35
, and
, M is the midpoint of
, the perimeter of trapezoid BMNC is
, and N is the
Regents Exam Questions G.G.42: Midsegments
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10 In the diagram below of
If
, and
and
are midsegments.
, determine and state the perimeter of quadrilateral FDEC.
11 In the diagram below of
If
1)
2)
3)
4)
,
, D is the midpoint of
, which expression represents DE?
, and E is the midpoint of
.
Regents Exam Questions G.G.42: Midsegments
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12 In
1)
2)
3)
4)
, D is the midpoint of
, what is the value of x?
and E is the midpoint of
and
6
7
9
12
13 In the diagram of
below, A is the midpoint of
the midpoint of
, and
and
are drawn.
If
1)
2)
3)
4)
. If
and
5
13
16
32
, what is the length of
, B is the midpoint of
?
, C is
Regents Exam Questions G.G.42: Midsegments
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14 Triangle ABC is shown in the diagram below.
If
1)
joins the midpoints of
and
, which statement is not true?
2)
3)
4)
15 In the diagram below,
joins the midpoints of two sides of
Which statement is not true?
1)
2)
3)
4)
area of
perimeter of
area of
perimeter of
.
Regents Exam Questions G.G.42: Midsegments
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16 On the set of axes below, graph and label
with vertices at
,
, and
. If G is the midpoint of
and H is the midpoint of
, state the coordinates of
G and H and label each point on your graph. Explain why
.
17 Triangle HKL has vertices
,
, and
. The midpoint of
is M and the
midpoint of
is N. Determine and state the coordinates of points M and N. Justify the
statement:
is parallel to
. [The use of the set of axes below is optional.]
Regents Exam Questions G.G.42: Midsegments
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1 ANS: 1
2 ANS: 1
REF: 010521a
REF: 081003ge
3 ANS:
REF: 081531ge
4 ANS:
37. Since
is a midsegment,
REF: 061030ge
5 ANS:
20
REF: 060929ge
6 ANS: 3
7 ANS: 4
REF: 080920ge
.
REF: 061211ge
8 ANS: 1
.
Regents Exam Questions G.G.42: Midsegments
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REF: 011413ge
9 ANS: 4
REF: 061520ge
10 ANS:
REF: 081430ge
11 ANS: 2
REF: 011103ge
12 ANS: 3
13
14
15
16
REF:
ANS:
ANS:
ANS:
ANS:
061311ge
3
3
3
REF: 081320ge
REF: 011311ge
REF: 081227ge
Regents Exam Questions G.G.42: Midsegments
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REF: fall0835ge
17 ANS:
.
REF: 011237ge
.
is a midsegment.