Answer:
Right scalene triangle
Acute equilateral triangle
Step-by-step explanation:
For the first triangle, we will use the Converse of the Pythagorean Theorem:
If c² < a² + b², then it means that it is an acute triangle.
If c² = a² + b², then it means that it is a right triangle.
If c² > a² + b², then it means that it is an obtuse triangle.
For the first triangle, let c = 25 yd, a = 7 yd, and b = 24 yd
c² = a² + b²
25² = 7² + 24²
625 = 49 + 576
625 = 625 (True statement).
Therefore, the first triangle is a right triangle. At the same time, each angle have different measures, making it a scalene triangle. Therefore, the first triangle is an example of a right scalene triangle.
For the second triangle, since all sides are equal, it doesn't matter which side we label as a, b, or c.
Let's see which type of triangle it is according to its sides:
c² = a² + b²
32² = 32² + 32²
1024 < 2048
Therefore, it is an acute triangle. At the same, the second triangle has equal sides, making it an equilateral triangle. Therefore, the second triangle is an example of an acute equilateral triangle.
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