55 points
Which of the following choices is the standard deviation of the sample shown
here?
19, 20, 21, 22, 23
O A. 22.5
B. 21
C. 2
D. 2.5
O E. 2

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

Abcd is reflected across the x- axis, then rotated 90 clockwise about the orgin, and finally reflected across the line y= x to form a’ b’ c’ .

Areflection of shape i across the y-axis, followed by a , and then a translation left 6 units and down 4 units confirms congruence between shape i and shape ii. alternatively, a of shape ii about the origin, followed by a reflection across the y-axis, and then a translation right 4 units and up 6 units confirms congruence between shape ii and shape i.