Podcast
Questions and Answers
What type of triangle has three acute angles?
What type of triangle has three acute angles?
- Obtuse triangle
- Right triangle
- Equilateral triangle (correct)
- Isosceles triangle
Which type of triangle contains an obtuse angle?
Which type of triangle contains an obtuse angle?
- Equilateral triangle
- Isosceles triangle
- Right triangle (correct)
- Acute triangle
How many sides of equal length does an isosceles triangle have?
How many sides of equal length does an isosceles triangle have?
- Two (correct)
- Four
- One
- Three
Which type of triangle has exactly one obtuse angle?
Which type of triangle has exactly one obtuse angle?
What are the angles within a triangle called?
What are the angles within a triangle called?
What is the sum of the interior angles of any triangle?
What is the sum of the interior angles of any triangle?
Why do all triangles have a total measurement of $180$ degrees?
Why do all triangles have a total measurement of $180$ degrees?
In an equilateral triangle, how much is the measurement of each angle?
In an equilateral triangle, how much is the measurement of each angle?
If one angle in an isosceles triangle is $80$ degrees, what is the measurement of the other two angles?
If one angle in an isosceles triangle is $80$ degrees, what is the measurement of the other two angles?
If angle A in a triangle measures $30$ degrees and angle B measures $60$ degrees, what is the measurement of angle C?
If angle A in a triangle measures $30$ degrees and angle B measures $60$ degrees, what is the measurement of angle C?
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Study Notes
Triangle Basics
- A triangle is a shape with three points and three lines that intersect at these points, containing a total of three interior angles.
- Interior angles are the angles within the triangle, and exterior angles are the angles that lie outside the triangle.
Types of Triangles
- Right triangles contain a right angle (90°).
- Acute triangles have three acute angles (less than 90°).
- Obtuse triangles have one angle that is greater than 90° (obtuse angle).
- Equilateral triangles have three equal sides and three equal angles.
- Isosceles triangles have two sides of the same length and two angles with the same measurement.
- Scalene triangles have sides that are all unique in size.
Angle Sum Property
- The sum of the interior angle measurements within a triangle always equals 180°.
- This is true for any and every triangle, regardless of type.
Why Triangles Have 180 Degrees
- A straight angle is an angle whose measurement is exactly 180°.
- If a straight angle is divided into three points, a triangle can be formed, and the sum of the interior angles still equals 180°.
Solving Unknown Angles
- If one angle measurement is unknown, it can be found by taking the sum of the other two angle measurements and subtracting it from 180°.
- Using the properties of the triangle type, one can also determine unknown angles.
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