With similar triangles, the corresponding angles are equal. True or False?

Mathematics

2 answers:

Svetradugi [14.3K]3 years ago

6 0

Answer: its true

i did this on apex too so i got you

Stels [109]3 years ago

5 0

Its true because of the rule (cpct)corresponding parts of congruence triangle.

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Answer:

a = $6*\sqrt{3}$

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Step-by-step explanation:

Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.

A 45-45-90 right triangle has side lengths $1-1-\sqrt{2}$ .

A 30-60-90 right triangle has side lengths $1 - \sqrt{3} -2$ .

Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.

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Side b corresponds to side length 2, b = 2*6 = 12.

The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to $\sqrt{2}$ . This means $\sqrt{2}$ was multiplied by $12 = \sqrt{2} * \sqrt{72}$ . This means that side c is $\sqrt{72}=6\sqrt{2}$ .