Question

Which statements must be true?

Select each correct answer.

See screenshot down below.

Answer 1

CA=1/2 of YZ, a is the mid point of xy and c is the mid point of xz. joining the mid point will give the answer, and a law is used here.

Answer 2

(1).
`\bar{CB}` ║
`\bar{XY}`

(2).
`\bar{AB}`║
`\bar{XZ}`

(3).
`CA=(1)/(2)*YZ`

Explanation:

The following statement must be true.

(1).
`\bar{CB}` ║
`\bar{XY}`

(2).
`\bar{AB}`║
`\bar{XZ}`

(3).
`CA=(1)/(2)*YZ`

Now, the reason of each above true statement as the following.

(1) In ΔXYZ, the line segment CB intersect the sides XZ and YZ in the same ratio hence it is parallel to the third side XY of the triangle XYZ (from Thales theorem).

(2).In ΔXYZ, the line segment AB intersect the sides XY and YZ in the same ratio hence it is parallel to the third side XZ of the triangle XYZ (from Thales theorem).

(3). In ΔXYZ, the line segment AC intersect the sides XY and XZ in the same ratio hence it is parallel to the third side YZ of the triangle XYZ (from Thales theorem). Here the ratio of intersected side is =1 (
`XA:AY=XC:CZ=1`) hence line segment AC is also the half of third side YZ.