Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
3. Section 2.3
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Exercise 88 Page 117

Practice makes perfect
a In a right triangle where the non-right angles are both 45^(∘), the legs are congruent.

Consequently, if the opposite side of an angle is longer than its adjacent side, the angle will be greater than 45^(∘), and vice-versa. Let's identify the opposite and adjacent side to x in our diagram.

Since the opposite side of x is less than the adjacent side, the measure of x must be less than 45^(∘).

b The triangle's legs are congruent, which means this is an isosceles triangle. Therefore, both non-right angles — which includes x — are 45^(∘).
c Like in Part A, we have to identify the opposite and adjacent side of the angle.

Since the opposite side is longer than the adjacent side, x must be greater than 45^(∘).