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Questions and Answers
Which type of triangle has two equal sides?
Which type of triangle has two equal sides?
- Right Triangle
- Equilateral Triangle
- Obtuse Triangle
- Isosceles Triangle (correct)
A straight angle measures less than 180 degrees.
A straight angle measures less than 180 degrees.
False (B)
What is the formula of the Pythagorean Theorem?
What is the formula of the Pythagorean Theorem?
a^2 + b^2 = c^2
An acute angle measures less than ___ degrees.
An acute angle measures less than ___ degrees.
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Match the types of angles with their definitions:
Match the types of angles with their definitions:
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What is the longest side of a right triangle called?
What is the longest side of a right triangle called?
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The sum of the interior angles of a triangle is always 180 degrees.
The sum of the interior angles of a triangle is always 180 degrees.
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What do you call the two sides that form the right angle in a right triangle?
What do you call the two sides that form the right angle in a right triangle?
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Study Notes
Basic Concepts in Geometry and Algebra
- Point: A location on a plane, having no dimensions; denoted with a capital letter.
- Line Segment: A part of a line with two endpoints and a definite length; represented by its endpoints.
- Ray: A line segment with an arrowhead at one end, indicating direction; starts from an initial point.
- Perpendicular Lines: Formed when two straight lines intersect, creating four equal angles.
- Angle: A geometric figure formed by two line segments or rays that meet at a common point.
Types of Angles
- Straight Angle: An angle that forms a straight line; measures exactly 180°.
- Acute Angle: Measures less than 90°.
- Obtuse Angle: Measures more than 90° but less than 180°.
- Reflex Angle: Measures more than 180° but less than 360°; an example is 270°.
Triangles
- Definition: A closed plane figure with three line segments which form three angles and three sides. The sum of the angles in a triangle is always 180°.
Types of Triangles
- Right Triangle: Contains one right angle (90°); the two sides forming the right angle are called legs, while the opposite side is the hypotenuse.
- Isosceles Triangle: Has two equal sides, with the angles opposite these sides also being equal.
- Isosceles Right Triangle: A special type of isosceles triangle with one right angle.
- Equilateral Triangle: All three sides and angles are equal, measuring 60° each.
Triangle Properties
- Exterior Angle: Equal to the sum of the two opposite interior angles of the triangle.
- Complementary Angles: The sum of two acute angles equals 90°.
- Supplementary Angles: The sum of two angles equals 180°.
Triangle Theorems
- SSS: Side, Side, Side criterion for triangle congruence.
- SAS: Side, Angle, Side criterion for triangle congruence.
- ASA: Angle, Side, Angle criterion for triangle congruence.
- AAS: Angle, Angle, Side criterion for triangle congruence.
- RHS: Right angle, Hypotenuse Side theorem for right triangles.
Other Triangle Terms
- Legs: The two sides that form the right angle in a right triangle.
- Hypotenuse: The longest side in a right triangle, opposite the right angle.
Pythagorean Theorem
- Describes the relationship in a right triangle where the sum of the squares of the legs (a² + b²) equals the square of the hypotenuse (c²).
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