Since bc is parallel to de, triangles abc and ade are similar. what are the lengths of the unknown sides? a. ac = 14 cm; ce = 8 cm b. ac = 12 cm; ce = 7 cm c. ac = 10 cm; ce = 5 cm d. ac = 5 cm; ce = 10 cm

C

Step-by-step explanation:

Step 1: find BC

Given Triangles ABC and ADE are similar,

=

BC = x DE

= x 9

= 6 cm

Step 2: use Pythagorean theorem to find AC and / or AE

Consider triangle ABC,

by Pythagorean theorem,

AB² + BC² = AC²

AC² = 6² + 8² = 100

AC = √100 = 10 (answer... we can see that C is the only one with AC=10.

Step 3: Verify.. even though we know that it is C because AC  = 10,  you can verify that the ansewer is correct by finding CE and confirming that CE=5

By using similar triangles ABC and ADE,

AC/AE = AB / AD

AE = AD/AB x AC = 12/8 x 10 = 15

CE = AE - AC = 15 - 10 = 5 (answer confirmed)

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap