G.CO.C.10.Midsegments - JMAP
1 In the diagram below of [pic], D, E, and F are the midpoints of [pic], [pic], and [pic], respectively.
[pic]
What is the ratio of the area of [pic] to the area of [pic]?
|1) |1:1 |
|2) |1:2 |
|3) |1:3 |
|4) |1:4 |
2 In the diagram below, the vertices of [pic] are the midpoints of the sides of equilateral triangle ABC, and the perimeter of [pic] is 36 cm.
[pic]
What is the length, in centimeters, of [pic]?
|1) |6 |
|2) |12 |
|3) |18 |
|4) |4 |
3 In isosceles triangle RST shown below, [pic], M and N are midpoints of [pic] and [pic], respectively, and [pic] is drawn. If [pic] and the perimeter of [pic] is 25, determine and state the length of [pic].
[pic]
4 In the diagram below of [pic], [pic] is a midsegment of [pic], [pic], [pic], and [pic]. Find the perimeter of [pic].
[pic]
5 In the diagram of [pic] below, [pic], [pic], and [pic]. Find the perimeter of the triangle formed by connecting the midpoints of the sides of [pic].
[pic]
6 In the diagram of equilateral triangle ABC shown below, E and F are the midpoints of [pic] and [pic], respectively.
[pic]
If [pic] and [pic], what is the perimeter of trapezoid ABFE?
|1) |36 |
|2) |60 |
|3) |100 |
|4) |120 |
7 In the diagram below of [pic], D is the midpoint of [pic], O is the midpoint of [pic], and G is the midpoint of [pic].
[pic]
If [pic], [pic], and [pic], what is the perimeter of parallelogram CDOG?
|1) |21 |
|2) |25 |
|3) |32 |
|4) |40 |
8 In the diagram of [pic] shown below, D is the midpoint of [pic], E is the midpoint of [pic], and F is the midpoint of [pic].
[pic]
If [pic], [pic], and [pic], what is the perimeter of trapezoid ABEF?
|1) |24 |
|2) |36 |
|3) |40 |
|4) |44 |
9 In [pic] shown below, L is the midpoint of [pic], M is the midpoint of [pic], and N is the midpoint of [pic].
[pic]
If [pic], [pic], and [pic], the perimeter of trapezoid BMNC is
|1) |35 |
|2) |31 |
|3) |28 |
|4) |26 |
10 As shown in the diagram below, M, R, and T are midpoints of the sides of [pic].
[pic]
If [pic], [pic], and [pic], what is the perimeter of quadrilateral ACRM?
|1) |35 |
|2) |32 |
|3) |24 |
|4) |21 |
11 In the diagram below, [pic], [pic], and [pic] are midsegments of [pic].
[pic]
The perimeter of quadrilateral ADEF is equivalent to
|1) |[pic] |
|2) |[pic] |
|3) |[pic] |
|4) |[pic] |
12 In the diagram below of [pic], [pic] and [pic] are midsegments.
[pic]
If [pic], and [pic], determine and state the perimeter of quadrilateral FDEC.
13 In the diagram below of [pic], D is the midpoint of [pic], and E is the midpoint of [pic].
[pic]
If [pic], which expression represents DE?
|1) |[pic] |
|2) |[pic] |
|3) |[pic] |
|4) |[pic] |
14 In [pic], D is the midpoint of [pic] and E is the midpoint of [pic]. If [pic] and [pic], what is the value of x?
[pic]
|1) |6 |
|2) |7 |
|3) |9 |
|4) |12 |
15 In the diagram of [pic] below, A is the midpoint of [pic], B is the midpoint of [pic], C is the midpoint of [pic], and [pic] and [pic] are drawn.
[pic]
If [pic] and [pic], what is the length of [pic]?
|1) |5 |
|2) |13 |
|3) |16 |
|4) |32 |
16 In quadrilateral ABCD below, [pic], and E, H, and F are the midpoints of [pic], [pic], and [pic], respectively.
[pic]
If [pic], [pic], and [pic], then FH is
|1) |9 |
|2) |10 |
|3) |12 |
|4) |21 |
17 Triangle ABC is shown in the diagram below.
[pic]
If [pic] joins the midpoints of [pic] and [pic], which statement is not true?
|1) |[pic] |
|2) |[pic] |
|3) |[pic] |
|4) |[pic] |
18 In the diagram below, [pic] joins the midpoints of two sides of [pic].
[pic]
Which statement is not true?
|1) |[pic] |
|2) |[pic] |
|3) |area of [pic] area of [pic] |
|4) |perimeter of [pic] perimeter of [pic] |
19 On the set of axes below, graph and label [pic] with vertices at [pic], [pic], and [pic]. If G is the midpoint of [pic] and H is the midpoint of [pic], state the coordinates of G and H and label each point on your graph. Explain why [pic].
[pic]
20 Triangle HKL has vertices [pic], [pic], and [pic]. The midpoint of [pic] is M and the midpoint of [pic] is N. Determine and state the coordinates of points M and N. Justify the statement: [pic] is parallel to [pic]. [The use of the set of axes below is optional.]
[pic]
1 ANS: 4 REF: 081716geo
2 ANS: 1
[pic]
REF: 081003ge
3 ANS:
[pic] [pic]
REF: 081531ge
4 ANS:
37. Since [pic] is a midsegment, [pic]. [pic]
REF: 061030ge
5 ANS:
20. The sides of the triangle formed by connecting the midpoints are half the sides of the original triangle. [pic]. [pic]
REF: 060929ge
6 ANS: 3
[pic] [pic]. Since [pic] is a midsegment, [pic]. Since [pic] is equilateral, [pic]. [pic]
REF: 061923geo
7 ANS: 3
[pic]
REF: 080920ge
8 ANS: 4
[pic]. [pic]
REF: 061211ge
9 ANS: 1
[pic]
REF: 011413ge
10 ANS: 1
[pic][pic]
REF: 011611ge
11 ANS: 4 REF: 011704geo
12 ANS:
[pic] [pic]
REF: 081430ge
13 ANS: 2
[pic]
REF: 011103ge
14 ANS: 3
[pic]
REF: 061311ge
15 ANS: 3 REF: 081320ge
16 ANS: 3
[pic]
REF: 012009geo
17 ANS: 3 REF: 011311ge
18 ANS: 3 REF: 081227ge
19 ANS:
[pic]
REF: fall0835ge
20 ANS:
[pic]. [pic]. [pic] is a midsegment. [pic]
REF: 011237ge
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