Mid Point Theorem

Which of the following is the statement of the Mid-point Theorem ?

• The line segment joining the mid-points of any two sides of a triangle is equal to the third side.

• The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to it.

• The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.

• The line segment joining the mid-points of any two sides of a triangle is twice the third side.

Tags

CCSS.HSG.SRT.B.4

In  $\Delta$  ABC, M is mid-point of AB and a straight line through M and parallel to BC cuts AC at N. If AC = 6 cm, then the length of AN is

• 3 cm

• 6 cm

• 12 cm

• Can not be determined

Tags

CCSS.HSG.SRT.B.4

In a trapezium ABCD, M and N are the mid-points of the non-parallel sides AD and BC respectively. If AB = 11 cm and DC = 8 cm, the length of MN is:

• $5\cdot5$ cm

• 4 cm

• 9 cm

• $9\cdot5\ cm$

 $In\ a\ \Delta$  ABC, X and Y are mid-points of the sides AB and AC respectively. If BC = 5 cm, AB = 7 cm and AC = 6 cm, the perimeter of trapezium XBCY is:

• 14 cm

• 18 cm

• 9 cm

• 16 cm

Tags

CCSS.HSG.SRT.B.4

 $In\ a\ \Delta$  ABC, D, E and F are the mid-points of the sides BC, CA and AB respectively. If AB = 5 cm, BC = 5.2 cm and CA = 6.4 cm, the perimeter of triangle DEF is:

•  $16\cdot6\ cm$  

•  $8\cdot4\ cm$  

•  $8\cdot2\ cm$  

•  $8\ \cdot3\ cm$  

Tags

CCSS.HSG.SRT.B.4

In the given figure, AE ll BF ll CG and D is the mid-point of CE . If AB = 4.2 cm, the length of BC is:

• $2\cdot1\ cm$

• $4\cdot2\ cm$

• $8\cdot4\ cm$

• 4 cm

Tags

CCSS.HSG.CO.C.10

In the given figure, AE ll BF ll CG and D is the mid-point of CE. Find the length of DF if CG = 7.8 cm

•  $3\cdot9\ cm$  

•  $3\cdot4\ cm$  

•  $4\cdot2\ cm$  

• 6 cm

Tags

CCSS.HSG.CO.C.10

The adjoining figure shows a trapezium ABCD in which

AB II DC. P is the mid-point of AD and PR II AB. Then, the relation between PR , AB and CD is:

• $PR\ =AB\ +CD$

• $PR\ =CD-AB$

• $PR\ =\frac{AB+CD}{2}$

• $PR\ =\frac{CD-AB}{2}$

In the given figure of triangle ABC , AM = BM , AN = 5 cm and BC = 7 cm. If MN II BC , find the length of AC and its correct reason :

• 5 cm; Mid-point Theorem

• 10 cm; Converse of Mid-point Theorem

• 7 cm; Equal Intercept Theorem

• 10 cm; Mid-point Theorem

Tags

CCSS.HSG.CO.C.10

In the given triangle ABC , AP = BP = 8 cm, AQ = CQ = 9 cm, BC = 6 cm and PQ = x cm. Then the value of x along with its correct reason is:

• 6 cm;Equal Intercept Theorem

• 3 cm; Mid-point Theorem

• 4 cm; Converse of Mid-point Theorem

• 4.5 cm; Mid-point Theorem

Tags

CCSS.HSG.CO.C.10