1. Which of the following best describes a HAMILTONIAN PATH.
A. A path that uses each VERTEX of a graph exactly once and ends at a vertex different from the starting vertex.
B. A path that uses each EDGE of a graph exactly once and ends at the starting vertex.
C. A path that uses each VERTEX of a graph exactly once and ends at the starting vertex.

2. Which of the below descriptions shows a possible HAMILTON PATH?
FEBCBAD <

3. Which of the following best describes a Hamiltonian Circuit.
A path that uses each VERTEX of a graph exactly once and ends at the starting vertex. <

4. Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph?
A. ABCDA
B. ACBDA
C. ADBCA

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality