C is the incenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABC and DBC are congruent? It is given that C is the incenter of triangle ABD, so segment BC is an altitude of angle ABD. Angles ABC and DBC are congruent according to the definition of an angle bisector. Segments AB and DB are congruent by the definition of an isosceles triangle. Triangles ABC and DBC share side BC, so it is congruent to itself by the reflexive property. By the SAS postulate, triangles ABC and DBC are congruent. Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD. There is an error in line 1; segment BC should be an angle bisector. The proof is correct. There is an error in line 3; segments AB and BC are congruent. There is an error in line 5; the ASA Postulate should be used.

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

Which of the following correctly justifies statement four of the two column proof? a. corresponding angles theorem b. transitive property of equality c. vertical angle theorem d. substitution property of equality

Find the unit rate for: 75% high-fiber chimp food to 25% high -protein chimp food.