Question 2 b
a
b
a
a
a2 a
16 Б
c
C
ca
c
C
b
b
b?
Which statement best explains
why the sum of the areas of the
two white squares in Figure 2 is
the same as the area of the white
square in Figure 1?
b
a
a b
Figure 1
ba
Figure 2.
The combined area of the four triangles is equal to the area of the large white
square.
In each triangle, the length of side a plus the length of side b equals the length
of side c. That means that a² + b2 = c?.
In each figure the total area is equal and the area of the 4 triangles is equal, so
the remaining white area in each fiqure must also be equal

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