Well, lets take a look at our options here. Option C is incorrect because PR doesn't equal SQ. D is wrong because it just tells us the same thing, which doesn't help us. A and B are our only answers. B is wrong because we can already see that the angle is a right angle, but we don't know if the hypo is the same, which is needed because without it, we can't tell what the other 2 angles are. A is the right answer.
C. â–łADE and â–łEBA
Let's look at the available options and see what will fit SAS.
A. â–łABX and â–łEDX
* It's true that the above 2 triangles are congruent. But let's see if we can somehow make SAS fit. We know that AB and DE are congruent, but demonstrating that either angles ABX and EDX being congruent, or angles BAX and DEX being congruent is rather difficult with the information given. So let's hold off on this option and see if something easier to demonstrate occurs later.
B. â–łACD and â–łADE
* These 2 triangles are not congruent, so let's not even bother.
C. â–łADE and â–łEBA
* These 2 triangles are congruent and we already know that AB and DE are congruent. Also AE is congruent to EA, so let's look at the angles between the 2 pairs of congruent sides which would be DEA and BAE. Those two angles are also congruent since we know that the triangle ACE is an Isosceles triangle since sides CA and CE are congruent. So for triangles â–łADE and â–łEBA, we have AE self congruent to AE, Angles DAE and BEA congruent to each other, and finally, sides AB and DE congruent to each other. And that's exactly what we need to claim that triangles ADE and EBA to be congruent via the SAS postulate.
Answer:
56 dgrees
Step-by-step explanation:
Answer:
6.6 miles
Step-by-step explanation:
due to the construction with the 3 parallel lines, the two crossing lines create 2 similar triangles (same angles and all side lengths and all other lines are all determined by the same multiplication factor going from one triangle to the other).
so,
LM = KL × f
MP = HK × f
HL = LP × f
KL = LM × f
and so on.
and then, also
JL = LN × f
the other thing we know due to the construction (L will always be connected with the middle of HK and MP) : the triangles are isoceles triangle (2 equal sides). in fact, because HK = HL = 2 miles, and it is an isoceles triangle, we also know that KL = 2 miles too.
so, we have
KL = LM × f
2 = 6 × f
f = 2/6 = 1/3
and therefore
JL = LN × f
2.2 = LN × 1/3
LN = 2.2 / 1/3 = 2.2 × 3/1 = 2.2 × 3 = 6.6
so, LN is 6.6 miles long.