Exploring Mid-Segment Theorem with Coordinates and Geometry

In triangle ABC, the midpoints of sides AB and AC are D and E, respectively. If AD = 5 cm and AE = 7 cm, what is the length of DE?

• 5 cm

• 8 cm

• 10 cm

• 3 cm

Tags

CCSS.HSG.SRT.B.4

Triangle PQR has vertices P(2, 3), Q(6, 7), and R(10, 3). Find the coordinates of the midpoints of sides PQ and PR, and determine the length of the segment connecting these midpoints.

• (4, 4) and (6, 2), length is √8

• (3, 5) and (7, 3), length is 3√2

• The midpoints are (4, 5) and (6, 3), and the length of the segment connecting them is 2√2.

• (5, 5) and (8, 3), length is 4

Tags

CCSS.HSG.GPE.B.6

In triangle XYZ, the midpoints of sides XY and XZ are M and N. If MN = 4 cm, what is the length of side YZ?

• 10 cm

• 12 cm

• 6 cm

• 8 cm

Tags

CCSS.HSG.SRT.B.4

A triangular park has vertices at A(1, 1), B(5, 1), and C(3, 4). Calculate the coordinates of the midpoints of sides AB and AC, and find the length of the segment connecting these midpoints.

• 1.4142

• 3.0000

• 2.2361

• 1.8028

Tags

CCSS.HSG.GPE.B.6

In triangle DEF, the midpoints of sides DE and DF are G and H. If DE = 10 cm and DF = 12 cm, what is the length of GH?

• 10 cm

• 11 cm

• 9 cm

• 13 cm

Tags

CCSS.HSG.SRT.B.4

Triangle JKL has vertices J(0, 0), K(4, 0), and L(2, 3). Find the midpoints of sides JK and JL, and calculate the distance between these midpoints.

• 3.6056

• 1.8028

• 1.4142

• 2.2361

Tags

CCSS.HSG.GPE.B.6

In triangle MNO, the midpoints of sides MN and MO are P and Q. If PQ = 6 cm, what is the length of side NO?

• 12 cm

• 10 cm

• 8 cm

• 14 cm

Tags

CCSS.HSG.SRT.B.4

A triangular garden has vertices at A(2, 2), B(6, 2), and C(4, 6). Determine the coordinates of the midpoints of sides AB and AC, and find the length of the segment connecting these midpoints.

• The length of the segment connecting the midpoints is 2.

• The length of the segment connecting the midpoints is sqrt(5).

• The length of the segment connecting the midpoints is sqrt(10).

• The length of the segment connecting the midpoints is 3.

Tags

CCSS.HSG.GPE.B.6

In triangle RST, the midpoints of sides RS and RT are U and V. If RS = 8 cm and RT = 10 cm, what is the length of UV?

• 5 cm

• 7 cm

• 6 cm

• 4.5 cm

Tags

CCSS.HSG.SRT.B.4

Triangle UVW has vertices U(1, 2), V(5, 6), and W(3, 4). Calculate the midpoints of sides UV and UW, and determine the length of the segment connecting these midpoints.

• 1.5

• sqrt(3)

• sqrt(2)

• 2

Tags

CCSS.HSG.GPE.B.6