Find the length of side x and side y given the triangles are similar

Which triangle congruence postulate or theorem justifies my claim that the steps i made using construction paper and scissors produce an isosceles triangle? was it sss, sas, asa, aas, or hl?

Given: ab ≅ cd and ad ≅ bc prove: abcd is a parallelogram. statements reasons 1. ab ≅ cd; ad ≅ bc 1. given 2. ac ≅ ac 2. reflexive property 3. △adc ≅ △cba 3. ? 4. ∠dac ≅ ∠bca; ∠acd ≅ ∠cab 4. cpctc 5. ∠dac and ∠bca are alt. int. ∠s; ∠acd and ∠cab are alt. int. ∠s 5. definition of alternate interior angles 6. ab ∥ cd; ad ∥ bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3? triangle angle sum theorem sas congruency theorem sss congruency theorem cpctc

Data on oxide thickness of semiconductors are as follows: 426 432 418 418 421 436 418 408 431 435 423 426 411 434 435 432 411 426 407 439 422 426 412 416 consider this data as a sample of the population. (a) calculate a point estimate of the mean oxide thickness for all wafers in the population. (round your answer to 3 decimal places.) (b) calculate a point estimate of the standard deviation of oxide thickness for all wafers in the population. (round your answer to 2 decimal places.) (c) calculate the standard error of the point estimate from part (a). (round your answer to 2 decimal places.) (d) calculate a point estimate of the median oxide thickness for all wafers in the population. (express your answer to 1 decimal places.) (e) calculate a point estimate of the proportion of wafers in the population that have oxide thickness greater than 430 angstrom. (round your answer to 4 decimal places.)