Answer:
c. Definition of altitude.
Step-by-step explanation:
We are given that segment QS is an altitude in ΔPQR and we are asked to find a justification used while proving the similarity of triangles ΔPSQ and ΔQSR.
Since we know that altitude meets opposite side at right angles. When QS will intersect line PR we will get two right triangles QSR and QSP right angled at S.
ΔPQR is similar to ΔPSQ as they both share angle P and right triangle. So their third angle should also be similar.
ΔPQR is similar to ΔQSR as they both share angle R and both have a right triangle at Q and S respectively. So they will have their third angle equal.
ΔPQR is similar to triangles ΔQSR and ΔPSQ. Therefore, ΔQSR is similar to ΔPSQ.
Therefore, by definition of altitude triangles ΔPSQ and ΔQSR are similar as ΔPSQ and ΔQSR are created from ΔPQR by altitude QS.
So lets say for example you have 4 remainder 2. To turn that into a decimal you have to divide the whole number by the remainder to make to fraction. So now you have 4 2/4 which is the same as 4 1/2. To turn the fraction into a decimal you do 100 divided by the denominator (2) which is 50, and then multiply by the top numerator (1). Now you add on the whole number (4) onto your other number/100 (50/100=0.5) to make 4.5.
Examples:
5 remainder 4:
4/5 = (100/5 x 4) 20 x 4 = 80
80/100=0.08
0.08 + 5= 5.08
If you have a denominator that goes into 10 easily (2, 4, 5, 10) then you just have to multiply the numerator (top number) by the same number as the bottom to make 10, and then just turn that into a decimal:
Example:
4 remainder 3:
3/4 x 2.5 = 7.5/10
=75/100 = 0.75
0.75 + 4 = 4.75
221
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225
227
229
241
243
245
247
249
261
263
265
267
269
281
283
285
287
289
421
423
425
427
429
441
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445
447
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461
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465
467
469
481
483
485
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489
621
623
625
627
629
641
643
645
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649
661
663
665
667
669
681
683
685
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689
821
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825
827
829
841
843
845
847
849
861
863
865
867
869
881
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889
80 three-digit numbers
(just to make sure, check)