How do I find the values of x & y without using the Pythagorean theorem? It’s okay if you use it to give me the answer however, I don’t understand how you wouldn’t use it.

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  23) x=20; y=10√3

  24) x=4√2; y=8

  25) x=12; y=3+6√3

Step-by-step explanation:

Recognize that all of the triangles involved here are one of the two "special" triangles. By previous use of the Pythagorean theorem, or your familiarity with the trig functions of the "special" angles 30°, 45°, 60°, you know the following side ratios:

  45°-45°-90° triangle: 1 : 1 : √2

  30°-60°-90° triangle: 1 : √3 : 2

Using these ratios, you can solve these figures "by inspection."

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23) x = 2((10√2)/√2) = 20

  y = √3((10√2)/√2) = 10√3

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24) x = 4√2

  y = (4√2)√2 = 8

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25) x = 6·2 = 12

y = 3 +6√3 . . . . . 3 units more than the longer leg of the 6 : 6√3 : 12 triangle

the answer is stop cheating on things stoopid

step-by-step explanation:

im eatin up the 44

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.