Theorem: A line parallel to one side of a triangle divides the other two proportionately. In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

The figure shows triangle ABC with segments DE and DF. Point D is on side AB, point E is on side AC and point F is on side BC.

Which statement can be proved true using the given theorem? (6 points)

Segment BD = 32
Segment BD = 36
Segment BF = 15
Segment BF = 18

Your friend uses c=50p to find the total cost, c, for the people, p, entering a local amusement park what is the unit rate and what does it represent in the context of the situation?

Answer each of the questions for the following diagram: 1. what type of angles are these? 2. solve for x. what does x equal? 3. what is the measure of the angles?

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