Question # 4
4. Multiple Representation Write a different equation to find the angle measures in Example 2. Will the answer be the same? Explain.
As we know that the sum of angles of a triangle is 180⁰.
In Mathematics, an equilateral triangle:
- is said to be a triangle in which all three sides are equal.
- All three internal angles of an equilateral triangle are also congruent to each other, each having 60° measure.
From the given equilateral triangle, the equation can be written as:
x + x + x = 180⁰
As each angle is 60°.
so
60° + 60° + 60° = 180⁰
Therefore, each angle measure = x = 60°.
Yes! the answer is same, as the sum of angles of a triangle is 180⁰. The reason is that an equilateral triangle is said to be a triangle in which all three sides are equal. All three internal angles are also congruent to each other, each having 60° measure.
Question # 5
5. Draw Conclusion Triangle ABC is a right triangle. What conclusion can you draw about the measure of the angles of the triangle.
- A right triangle, let say ∠ABC, has two legs and a hypotenuse. The two legs meet at right angle - or 90° angle.
- The longest side is called the the hypotenuse is the longest side of the right triangle which is the opposite the right angle.
The Pythagorean Theorem defines the relationship in every right triangle such as:
A right isosceles triangle - having two same sides - has a 90° angle and two 90° angles.
Another kind of right triangle is the 30-60-90 degree triangle. Where one angle is right, 90°, and other two angles are 30° and 60°.
Another kind of right triangle is the 45-45-90 degree triangle. Where one angle is right, 90°, and other two angles are 45° and 45°.
So, we conclude that we have a variety of right triangles where one angle is the right angle, measuring 90° angle.