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Justify each statement with a property from algebra or property of congruence $∠Pâ‰\dots ∠P$.

a. In each exercise use the information given to conclude that two angles are congruent.

b. Name or state the definition or theorem that justifies your conclusion.

∠6 is complementary to ∠10; ∠7 is complementary to ∠10.

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a number is divisible by 4, then it is divisible by 6.

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If , then

Provide a counterexample to show that each statement is false.

Statement: If $n^2=5n$then $n=5$.

Provide a counterexample to show that each statement is false.

Statement: If point G is on $\stackrel{→}{AB}$,then G is on$\stackrel{→}{BA}$.

Copy and complete the proof of Theorem 2-6: If the exterior of two adjacent acute angles is perpendicular, then the angles are complementary.

Given:$\stackrel{→}{OA}âŠ\yen \stackrel{→}{OC}$

Prove: $∠AOB$and $∠BOC$are comp. $∠s$.

Proof:

The coordinates of points L and X are 16 and 40 respectively. N is the midpoint of $\stackrel{¯}{LX}$, and Y is the midpoint of $\stackrel{¯}{LN}$.

Sketch a diagram and find:

a. LN.

b. The coordinate of N.

c. LY.

d. the coordinate of Y.

State the converse of each conditional. Is the converse true or false?

If a number is divisible by 6, then it is divisible by 3.

Provide a counterexample to show that each statement is false.

Statement: If $xy>5y$, than $x>5$.