Determine whether Triangle AWT= UYZ. explain your reasoning ​

The triangles are congruent by the HL theorem

HL = hypotenuse leg

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Explanation:

Through the segment addition postulate, we can say:

WZ = WT+TZ

YT = TZ+ZY

Notice how both WZ and YT have TZ as part of their segments.

Since WZ and YT are the same length, we can then say,

WZ = YT

WT+TZ = TZ+ZY

WT = ZY

I used substitution for the second step.

The last step is where I subtracted TZ from both sides, and they canceled out.

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We have the following info:

Normally, the conclusion from here would be "not enough info" because this is a SSA case. Note how the angles are not between the congruent sides. So we wouldn't use SAS.

However, despite us having SSA, it doesn't mean we can't keep going. The reason why is because we have two right triangles. So we can use the HL theorem instead. Statement 1 above refers to the L of HL, while statement 2  is the H.

HL = hypotenuse leg

Again, HL only works for right triangles. It's the only time we can use SSA to prove right triangles are congruent; otherwise, SSA is not a valid congruence theorem.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

answer: it is d

step-by-step explanation: