3. Special Right Triangles
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Start with recalling the properties of special right triangles.
Variable | Value |
---|---|
x | 6 |
y | 10 |
z | 63 |
Perimeter: 38+62+63
Let's begin by reviewing the properties of special right triangles.
45∘- 45∘- 90∘ Triangle | 30∘- 60∘- 90∘ Triangle |
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In a 45∘- 45∘- 90∘ triangle, the legs ℓ are congruent and the hypotenuse h is 2 times the length of a leg. | In a 30∘- 60∘- 90∘ triangle, the hypotenuse h is 2 times the length of the shorter leg s, and the longer leg ℓ is 3 times the length of the shorter leg. |
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Now let's take a look at the given picture. We will name the missing vertices.
First of all, we can see that SR and TU are congruent as SRTU is a rectangle. Therefore, the value of y is also 10.
Let's notice that ST and RU are congruent. Therefore, the length of ST is 6. As we can see, △PST is a 45∘- 45∘- 90∘ triangle, so the length of PT is also 6 and the length of PS is 62.