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Answer:
- (a) Yes, AA postulate
- (b) SSS theorem
- long side: 35; total perimeter: 80
Step-by-step explanation:
1. Both triangles are right triangles, and the vertical angles at C are the same measure. Hence, the triangles are similar because they have two congruent angles: the AA postulate applies.
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2. The shortest-to-longest side ratios are ...
3 : 6 : 7
18 : 36 : 42 = 6(3) : 6(6) : 6(7) = 3 : 6 : 7
Corresponding sides are proportional, so the SSS theorem applies.
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3. Larger triangle side lengths are a factor of 5 times those of the smaller triangle. The missing side of the larger triangle is 5×7 = 35. The total perimeter of the larger triangle is 20+25+35 = 80. The required length of fence depends on what is being fenced (not specified).
