Question

A conjecture and the flowchart proof used to prove the conjecture are shown.Drag an expression or phrase to each box to complete the proof.

Answer 1

Solution: The solution is shown is below figure.

Step-by-step explanation:

From the given information JKLM is a parallelogram and
`\underset{LN}{\rightarrow}` bisects
`\angle KLP`. So Blank 1 is filled by Given and blank 2 is filled by
`\underset{LN}{\rightarrow}` bisects
`\angle KLP`.

Parallelogram is a quadrilateral whose opposite sides are equal or parallel. Since it is given that JKLM is a parallelogram, therefore the side JM is parallel to the side KL. So blank 3 filled by Definition of parallelogram.

If a line bisects an angle it is means it divides the angle in two equal parts. Since
`\underset{LN}{\rightarrow}` bisects
`\angle KLP`, therefore
`\angle 2\cong \angle 3`. Hence the blank 4 is filled by Definition of bisect.

The transitive property of congruence states that if
`\angle 1\cong \angle 2` and
`\angle 2\cong \angle 3`, then
`\angle 1\cong \angle 3`. Thus, the blank 5 is filled by Transitive Property of Congruence.