Question

aviation two airplanes are flying search patterns, as described:

• one airplane flies 5 miles due south from its base, turns 90° and flies due west for 10 miles, then returns directly to base.
• the second aircraft flies 10 miles due east from its base, turns 90° and flies 5 miles due south, then returns directly to its base.

which theorem of right triangle congruence can be used to show that both airplanes fly the same distance?
select choice theorem
select choice
la
ll
ha
hl

Explanation:

• For the first airplane, the two legs of the right - triangle formed by its path are \(a = 5\) miles and \(b=10\) miles.
• For the second airplane, the two legs of the right - triangle formed by its path are also \(a = 5\) miles and \(b = 10\) miles.
• The LL (Leg - Leg) congruence theorem for right - triangles states that if the legs of one right - triangle are congruent to the legs of another right - triangle, then the two right - triangles are congruent.
• Since the two right - triangles (formed by the paths of the two airplanes) have congruent legs, by the LL theorem, the hypotenuses (the return paths) are congruent. And the total distance each airplane flies is the sum of the lengths of the two legs and the hypotenuse. Since the legs and hypotenuses are congruent, the total distances are the same.

Answer:

LL (Leg - Leg)