Enhance Your Learning with Maths Special Triangle Flash Cards for quick learning
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Triangles with angles that are multiples of 30° and 45°, which have special ratios between their side lengths.
Ratios of the side lengths in a right triangle, including sine, cosine, and tangent.
Trigonometric functions that relate the angles of a right triangle to the ratios of its side lengths.
Functions that give the angle measures in a right triangle when the ratios of its side lengths are known.
Using special triangles to solve real-world problems involving angles, distances, and heights.
Properties of triangles that have the same shape (similarity) or the same size and shape (congruence).
Calculating the area (space inside) and perimeter (total length of sides) of triangles.
Relationships between circles and triangles, including the properties of triangles inscribed in circles.
Applying triangle concepts to solve word problems involving real-life scenarios.
A special right triangle with two 45° angles and one 90° angle, where the lengths of the sides are in a ratio of 1:1:√2.
A special right triangle with one 30° angle, one 60° angle, and one 90° angle, where the lengths of the sides are in a ratio of 1:√3:2.
The ratio of the length of the side opposite the angle θ to the length of the hypotenuse in a right triangle.
The ratio of the length of the side adjacent to the angle θ to the length of the hypotenuse in a right triangle.
The ratio of the length of the side opposite the angle θ to the length of the side adjacent to the angle θ in a right triangle.
The inverse trigonometric function that gives the angle whose sine is a given value.
The inverse trigonometric function that gives the angle whose cosine is a given value.
The inverse trigonometric function that gives the angle whose tangent is a given value.
Using trigonometric ratios to find the lengths of missing sides in a right triangle.
Using inverse trigonometric functions to find the measures of missing angles in a right triangle.
Triangles that have the same shape but different sizes, where the ratios of corresponding side lengths are equal.
Triangles that have the same size and shape, where all corresponding angles and side lengths are equal.
The amount of space inside a triangle, calculated using the formula A = 1/2 * base * height.
The total length of the sides of a triangle, calculated by adding the lengths of all three sides.
The distance around the edge of a circle, calculated using the formula C = 2πr or C = πd.
An angle whose vertex is on the circle and whose sides intersect the circle at two different points.
A triangle whose vertices are on the circle, with one side as a chord of the circle.
Real-world problems that require the application of triangle concepts to find solutions.
The branch of trigonometry that focuses on right triangles and their ratios.
Theorems that state conditions for triangles to be similar, such as the Angle-Angle (AA) and Side-Angle-Side (SAS) theorems.
Theorems that state conditions for triangles to be congruent, such as the Side-Side-Side (SSS) and Angle-Side-Angle (ASA) theorems.
A formula for calculating the area of a triangle when the lengths of all three sides are known.
A trigonometric law that relates the ratios of the side lengths to the sines of the opposite angles in any triangle.
A trigonometric law that relates the side lengths and angles of a triangle, allowing the calculation of missing side lengths or angle measures.
The ratio of the lengths of corresponding sides in similar triangles.
Statements that describe conditions for triangles to be congruent, such as the Side-Angle-Side (SAS) and Angle-Side-Angle (ASA) postulates.
A theorem that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Transformations that preserve the shape of a figure but change its size, such as dilation and similarity.
Transformations that preserve both the shape and size of a figure, such as translation, rotation, and reflection.
A line segment drawn from a vertex of a triangle perpendicular to the opposite side, forming a right angle.
A line segment drawn from a vertex of a triangle to the midpoint of the opposite side.
A line segment or ray that divides an angle of a triangle into two congruent angles.
The point of concurrency of the medians of a triangle, which is also the center of mass of the triangle.
The point of concurrency of the perpendicular bisectors of the sides of a triangle, which is equidistant from the three vertices.
The point of concurrency of the angle bisectors of the angles of a triangle, which is equidistant from the three sides.
The point of concurrency of the altitudes of a triangle, which is the intersection of the three altitudes.
A line that passes through the centroid, circumcenter, and orthocenter of a triangle.
A set of three positive integers (a, b, c) that satisfy the Pythagorean Theorem, a² + b² = c².
Polygons that have the same shape but different sizes, where the ratios of corresponding side lengths are equal.
Polygons that have the same size and shape, where all corresponding angles and side lengths are equal.
The amount of space inside a circle, calculated using the formula A = πr².
The amount of space inside a sector of a circle, calculated using the formula A = (θ/360°) * πr².
The length of an arc of a circle, calculated using the formula L = (θ/360°) * 2πr.
A line segment with both endpoints on the circle.
A line that intersects a circle at two points.
A line that intersects a circle at exactly one point, forming a right angle with the radius at that point.
A circle that is tangent to all three sides of a triangle.
A circle that passes through all three vertices of a triangle.
Properties and relationships involving circles, such as the Inscribed Angle Theorem and the Tangent-Secant Theorem.
Equations that describe the properties and relationships of circles, such as the equation of a circle and the equation of a tangent line.
Geometric constructions involving circles, such as constructing tangents and inscribed circles.
Regions of a circle bounded by two radii and an arc.
Regions of a circle bounded by a chord and an arc.
Lines that intersect a circle at exactly one point, forming a right angle with the radius at that point.
Points where two or more circles intersect.
Characteristics and relationships of circles, such as radius, diameter, circumference, and area.
Mathematical proofs that involve properties and relationships of circles.
Transformations that preserve the shape and size of a circle, such as translation, rotation, and reflection.
Symmetry properties of circles, such as rotational symmetry and reflectional symmetry.
Points of interest in a circle, such as the center, circumcenter, and incenter.
Line segments from the center of a circle to any point on the circle.
A line segment that passes through the center of a circle and has both endpoints on the circle.