Question

Determine if each statement is true or false based on the diagram.

Answer 1

Explanation:

1). JL = 36

Reason : Since, PN is the segment joining midpoints of sides JK and LK,

Therefore, JL = 2(PN)

JL = 2(36)

JL = 72

False.

2). ML = 36

Reason: Since, ML =
`(1)/(2)(JL)`

ML =
`(1)/(2)(72)`

= 36

True.

3). MP = 48.5

Reason : By the same property, MP =
`(1)/(2)(LK)`

MP =
`(97)/(2)`

MP = 48.5

True.

4). ∠JLK = 102°

Reason: Segment joining midpoints of two sides of a triangle is parallel and measures half of the third side of the triangle.

Since, PM║LK and JL is a transversal line,

∠JMP ≅ ∠JLK [Corresponding angles]

m∠JLK = 102°

True.

5). ∠PNK = 102°

Reason : Since, PN║JL and LK is a transversal line,

∠JLK ≅ ∠PNK [Corresponding angles]

∠PNK = 102°

True.

6). MP║PK

Reason : MP and PK are intersecting each other at P.

Therefore, they can not be parallel.

False.