Maths Special Triangle Study Cards

Enhance Your Learning with Maths Special Triangle Flash Cards for quick learning



Pythagorean Theorem

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.

Special Right Triangles

Triangles with angles that are multiples of 30° and 45°, which have special ratios between their side lengths.

Trigonometric Ratios

Ratios of the side lengths in a right triangle, including sine, cosine, and tangent.

Sine, Cosine, and Tangent

Trigonometric functions that relate the angles of a right triangle to the ratios of its side lengths.

Inverse Trigonometric Functions

Functions that give the angle measures in a right triangle when the ratios of its side lengths are known.

Applications of Special Triangles

Using special triangles to solve real-world problems involving angles, distances, and heights.

Similarity and Congruence

Properties of triangles that have the same shape (similarity) or the same size and shape (congruence).

Area and Perimeter

Calculating the area (space inside) and perimeter (total length of sides) of triangles.

Circles and Inscribed Triangles

Relationships between circles and triangles, including the properties of triangles inscribed in circles.

Word Problems

Applying triangle concepts to solve word problems involving real-life scenarios.

45-45-90 Triangle

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.

30-60-90 Triangle

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.

Sinθ

The ratio of the length of the side opposite the angle θ to the length of the hypotenuse in a right triangle.

Cosθ

The ratio of the length of the side adjacent to the angle θ to the length of the hypotenuse in a right triangle.

Tanθ

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.

Arcsin

The inverse trigonometric function that gives the angle whose sine is a given value.

Arccos

The inverse trigonometric function that gives the angle whose cosine is a given value.

Arctan

The inverse trigonometric function that gives the angle whose tangent is a given value.

Finding Missing Side Lengths

Using trigonometric ratios to find the lengths of missing sides in a right triangle.

Finding Missing Angle Measures

Using inverse trigonometric functions to find the measures of missing angles in a right triangle.

Similar Triangles

Triangles that have the same shape but different sizes, where the ratios of corresponding side lengths are equal.

Congruent Triangles

Triangles that have the same size and shape, where all corresponding angles and side lengths are equal.

Area of a Triangle

The amount of space inside a triangle, calculated using the formula A = 1/2 * base * height.

Perimeter of a Triangle

The total length of the sides of a triangle, calculated by adding the lengths of all three sides.

Circumference of a Circle

The distance around the edge of a circle, calculated using the formula C = 2πr or C = πd.

Inscribed Angle

An angle whose vertex is on the circle and whose sides intersect the circle at two different points.

Inscribed Triangle

A triangle whose vertices are on the circle, with one side as a chord of the circle.

Word Problems Involving Triangles

Real-world problems that require the application of triangle concepts to find solutions.

Right Triangle Trigonometry

The branch of trigonometry that focuses on right triangles and their ratios.

Similarity Theorems

Theorems that state conditions for triangles to be similar, such as the Angle-Angle (AA) and Side-Angle-Side (SAS) theorems.

Congruence Theorems

Theorems that state conditions for triangles to be congruent, such as the Side-Side-Side (SSS) and Angle-Side-Angle (ASA) theorems.

Heron's Formula

A formula for calculating the area of a triangle when the lengths of all three sides are known.

Law of Sines

A trigonometric law that relates the ratios of the side lengths to the sines of the opposite angles in any triangle.

Law of Cosines

A trigonometric law that relates the side lengths and angles of a triangle, allowing the calculation of missing side lengths or angle measures.

Similarity Ratio

The ratio of the lengths of corresponding sides in similar triangles.

Congruence Postulates

Statements that describe conditions for triangles to be congruent, such as the Side-Angle-Side (SAS) and Angle-Side-Angle (ASA) postulates.

Triangle Inequality Theorem

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.

Similarity Transformations

Transformations that preserve the shape of a figure but change its size, such as dilation and similarity.

Congruence Transformations

Transformations that preserve both the shape and size of a figure, such as translation, rotation, and reflection.

Altitude of a Triangle

A line segment drawn from a vertex of a triangle perpendicular to the opposite side, forming a right angle.

Median of a Triangle

A line segment drawn from a vertex of a triangle to the midpoint of the opposite side.

Angle Bisector of a Triangle

A line segment or ray that divides an angle of a triangle into two congruent angles.

Centroid of a Triangle

The point of concurrency of the medians of a triangle, which is also the center of mass of the triangle.

Circumcenter of a Triangle

The point of concurrency of the perpendicular bisectors of the sides of a triangle, which is equidistant from the three vertices.

Incenter of a Triangle

The point of concurrency of the angle bisectors of the angles of a triangle, which is equidistant from the three sides.

Orthocenter of a Triangle

The point of concurrency of the altitudes of a triangle, which is the intersection of the three altitudes.

Euler Line

A line that passes through the centroid, circumcenter, and orthocenter of a triangle.

Pythagorean Triple

A set of three positive integers (a, b, c) that satisfy the Pythagorean Theorem, a² + b² = c².

Similar Polygons

Polygons that have the same shape but different sizes, where the ratios of corresponding side lengths are equal.

Congruent Polygons

Polygons that have the same size and shape, where all corresponding angles and side lengths are equal.

Area of a Circle

The amount of space inside a circle, calculated using the formula A = πr².

Area of a Sector

The amount of space inside a sector of a circle, calculated using the formula A = (θ/360°) * πr².

Arc Length

The length of an arc of a circle, calculated using the formula L = (θ/360°) * 2πr.

Chord

A line segment with both endpoints on the circle.

Secant

A line that intersects a circle at two points.

Tangent

A line that intersects a circle at exactly one point, forming a right angle with the radius at that point.

Circle Inscribed in a Triangle

A circle that is tangent to all three sides of a triangle.

Circumscribed Circle of a Triangle

A circle that passes through all three vertices of a triangle.

Circle Theorems

Properties and relationships involving circles, such as the Inscribed Angle Theorem and the Tangent-Secant Theorem.

Circle Equations

Equations that describe the properties and relationships of circles, such as the equation of a circle and the equation of a tangent line.

Circle Constructions

Geometric constructions involving circles, such as constructing tangents and inscribed circles.

Circle Sectors

Regions of a circle bounded by two radii and an arc.

Circle Segments

Regions of a circle bounded by a chord and an arc.

Circle Tangents

Lines that intersect a circle at exactly one point, forming a right angle with the radius at that point.

Circle Intersections

Points where two or more circles intersect.

Circle Properties

Characteristics and relationships of circles, such as radius, diameter, circumference, and area.

Circle Proofs

Mathematical proofs that involve properties and relationships of circles.

Circle Transformations

Transformations that preserve the shape and size of a circle, such as translation, rotation, and reflection.

Circle Symmetry

Symmetry properties of circles, such as rotational symmetry and reflectional symmetry.

Circle Centers

Points of interest in a circle, such as the center, circumcenter, and incenter.

Circle Radii

Line segments from the center of a circle to any point on the circle.

Circle Diameter

A line segment that passes through the center of a circle and has both endpoints on the circle.