Questions and Answers
The angles of a straight line always equal...
180⁰
The sum of angles in any triangle will always equal...
180⁰
The sum of all interior angles of any polygon will always equal...
(n-2)×180
The sum of exterior angles of any polygon will always equal...
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An exterior angle plus its corresponding interior angle will always equal...
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A given exterior angle of a triangle will equal...
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Area of a triangle always equals...
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What is the Pythagorean Theorem?
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The lengths of the legs of every 30⁰: 60⁰: 90⁰ triangle always have the ratio...
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The lengths of the legs of every right isosceles triangle will have the ratio...
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The length of the third side of a triangle must be...
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List a family of triangles in the 3:4:5 ratio.
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Study Notes
Straight Line Angles
- Angles on a straight line total 180⁰.
Triangle Angle Sum
- The sum of all angles in any triangle (∆) equals 180⁰.
Polygon Interior Angles
- Interior angles of a polygon total (n-2)×180, where n equals the number of sides and (n-2) represents the number of triangles formed.
Polygon Exterior Angles
- The sum of the exterior angles of any polygon is always 360⁰, with one exterior angle per vertex.
Corresponding Angles
- Each exterior angle corresponds with its interior angle for a total of 180⁰, creating a straight line.
Triangle Exterior Angle Rule
- An exterior angle of a triangle equals the sum of its two opposite interior angles.
Triangle Area
- Area of a triangle is calculated using the formula 1/2bh (base × height).
Pythagorean Theorem
- In right triangles, a² + b² = c², where c is the hypotenuse. If this holds true, the triangle is right-angled; if not, it's not.
30-60-90 Triangle
- In a 30⁰: 60⁰: 90⁰ triangle, the leg lengths follow the ratio x: x√3: 2x, with x opposite the 30⁰ angle and 2x opposite the 90⁰ angle.
45-45-90 Triangle
- A right isosceles triangle (45⁰: 45⁰: 90⁰) has leg lengths in the ratio x: x: x√2. The hypotenuse can be set to √2 for calculation or halved and multiplied by √2.
3-4-5 Triangle Rule
- Classic Pythagorean triples include 3-4-5 ∆ (3² + 4² = 5²) and 5-12-13 ∆ (5² + 12² = 13²), with common multiples like 6:8:10.
Triangle Inequality Theorem
- The length of the third side of any triangle must be greater than the absolute difference of the other two sides and less than their sum.
3-4-5 Triangle Family
- Related triples include 6:8:10, 9:12:15, 12:16:20, and 15:20:25, all derived from the 3-4-5 relationship.
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Test your knowledge of basic geometry rules with these flashcards! Each card presents a fundamental principle, such as the sum of angles in lines, triangles, and polygons. Perfect for students eager to internalize these essential concepts in geometry.
