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.

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.