Geometry Vocabulary Unit-4
Centroid of a triangle
A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle. The centroid is also called the center of gravity of the triangle.
Scale drawing
A drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale). The scale is shown as the length in the drawing, then a colon (":"), then the matching length on the real thing.
Legs
A leg of a triangle is one of its sides. For a right triangle, the term "leg" generally refers to a side other than the one opposite the right angle (which is termed the hypotenuse). Legs are also known as catheti. SEE ALSO: Cathetus, Hypotenuse, Triangle.
Mid-segment
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.
Equidistant
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal. In two-dimensional Euclidean geometry the locus of points equidistant from two given (different) points is their perpendicular bisector.
Scalene triangle
A scalene triangle is a triangle that has three unequal sides, such as those illustrated above. SEE ALSO: Acute Triangle, Equilateral Triangle, Isosceles Triangle, Obtuse Triangle, Triangle. CITE THIS AS: Weisstein, Eric W. "
Corollary
A statement that follows with little or no proof required from an already proven statement. For example, it is a theorem in geometry that the angles opposite two congruent sides of a triangle are also congruent. A corollary to that statement is that an equilateral triangle is also equiangular.
Equiangular triangle
An equiangular triangle is a triangle where all three interior angles are equal in measure. Because the interior angles of any triangle always add up to 180°, each angle is always a third of that, or 60° ... See Equilateral Triangles.
Include angles
An included angle is the angle between two sides of a triangle. It can be any angle of the triangle, depending on its purpose. The included angle is used in proofs of geometric theorems dealing with congruent triangles. Congruent triangles are two triangles whose sides and angles are equal to each other.
Include side
Definition: The common leg of two angles. Usually found in triangles and other polygons, the included side is one that links two angles together. Think of it as being 'included' between two angles.
Hypotenuse
From Greek "to stretch" Definition: The longest side of a right triangle. The side opposite the right angle. In a right triangle (one where one interior angle is 90°), the longest side is called the hypotenuse.
Legs of an isosceles triangle
In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.
Vertex angle of an isosceles triangle
In an isosceles triangle, we have two sides called the legs and a third side called the base. The angle located opposite the base is called the vertex. Sample A: The vertex angle B of isosceles triangle ABC is 120 degrees.
Median of a triangle
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
Altitude of a triangle
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude.
Equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
Isosceles triangle
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Ratio
In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Since the two base angles
Isosceles TriangleFrom Greek: isos - "equal" , skelos - "leg" A triangle which has two of its sides equal in length. Try this Drag the orange dots on each vertex to reshape the triangle. Notice it always remains an isosceles triangle, the sides AB and AC always remain equal in length The word isosceles is pronounced "eye-sos-ell-ease" with the emphasis on the 'sos'. It is any triangle that has two sides the same length. If all three sides are the same length it is called an equilateral triangle. Obviously all equilateral triangles also have all the properties of an isosceles triangle. Properties The unequal side of an isosceles triangle is usually referred to as the 'base' of the triangle. The base angles of an isosceles triangle are always equal. In the figure above, the angles ∠ABC and ∠ACB are always the same When the 3rd angle is a right angle, it is called a "right isosceles triangle". The altitude is a perpendicular distance from the base to the topmost vertex. Constructing an Isosceles Triangle It is possible to construct an isosceles triangle of given dimensions using just a compass and straightedge. See these three constructions: Isosceles triangle, given base and side Isosceles triangle, given base and altitude Isosceles triangle, given leg and apex angle Solving an isosceles triangle The base, leg or altitude of an isosceles triangle can be found if you know the other two. A perpendicular bisector of the base forms an altitude of the triangle as shown on the right. This forms two congruent right triangles that can be solved using Pythagoras' Theorem as shown below. Finding the base To find the base given the leg and altitude, use the formula: Base = 2 √ L 2 − A 2 where: L is the length of a leg A is the altitude Finding the leg To find the leg length given the base and altitude, use the formula: Leg = √ A 2 + B 2 2 where: B is the length of the base A is the altitude Altitude To find the altitude given the base and leg, use the formula: Altitude = √ L 2 − B 2 2 where: L is the length of a leg B is the base Interior angles apex angle of isosceles triangle If you are given one interior angle of an isosceles triangle you can find the other two. For example, We are given the angle at the apex as shown on the right of 40°. We know that the interior angles of all triangles add to 180°. So the two base angles must add up to 180-40, or 140°. Since the two base angles are congruent (same measure), they are each 70°. base angle of isosceles triangle If we are given a base angle of say 45°, we know the base angles are congruent (same measure) and the interior angles of any triangle always add to 180°. So the apex angle must be 180-45-45 or 90°. Other triangle topics General Triangle definition Hypotenuse Triangle interior angles Triangle exterior angles Triangle exterior angle theorem Pythagorean Theorem Proof of the Pythagorean Theorem Pythagorean triples Triangle circumcircle Triangle incircle Triangle medians Triangle altitudes Midsegment of a triangle Triangle inequality Side / angle relationship Perimeter / Area Perimeter of a triangle Area of a triangle Heron's formula Area of an equilateral triangle Area by the "side angle side" method Area of a triangle with fixed perimeter Triangle types Right triangle Isosceles triangle Scalene triangle Equilateral triangle Equiangular triangle Obtuse triangle Acute triangle 3-4-5 triangle 30-60-90 triangle 45-45-90 triangle Triangle centers Incenter of a triangle Circumcenter of a triangle Centroid of a triangle Orthocenter of a triangle Euler line Congruence and Similarity Congruent triangles Solving triangles Solving the Triangle Law of sines Law of cosines Triangle quizzes and exercises Triangle type quiz Ball Box problem How Many Triangles? Satellite Orbits (C) 2011 Copyright Math Open Reference. All rights reserved
Volume
Math Term Definition. Volume. Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. It's units are always "cubic", that is, the number of little element cubes that fit inside the figure.
Similar polygons
Math definition of Similar Polygons: Similar Polygons - Two polygons whose corresponding angles are congruent and the lengths of the corresponding sides are proportional. Subject : Math. Topic : Geometry.
Right triangle
Right triangle. A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). ... The side opposite the right angle is called the hypotenuse (side c in the figure).
Scale
Scale. more ... The ratio of the length in a drawing (or model) to the length of the real thing. Example: in the drawing anything with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.
SSS postulate
Side Side Side Postulate. Proving Congruent Triangles with SSS. Side Side Side postulate states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
Base angles of an isosceles triangle
Since the two base angles are congruent (same measure), they are each 70°. If we are given a base angle of say 45°, we know the base angles are congruent (same measure) and the interior angles of any triangle always add to 180°. So the apex angle must be 180-45-45 or 90°.
ASA postulate
The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. (The included side is the side between the vertices of the two angles.)
AAS postulate
The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included angle of another triangle, then these two triangles are congruent.
SAS postulate
The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
Triangle inequality theorem
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Circumcenter of a triangle
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. It is also the center of the circumcircle, the circle that passes through all three vertices of the triangle. A Euclidean construction.
Proportion
The definition of geometrical proportion is the relationship between two things when the quantities of the two are equal in ratios. An example of geometrical proportion is when 4 is to 2 as 8 is to 4 - a square 4x2 and a square 8x4.
Exterior Angle theorem
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.
HL theorem
The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
Hypotenuse-leg theorem
The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
Perimeter
The perimeter of a figure is the total distance around the edge of the figure. For example, a square whose sides are 6 inches long has a perimeter of 6 x 4 = 24 inches because it has 4 sides 6 inches long. A rectangle whose length and width are 4 meters and 3 meters has a perimeter of 4 + 4 + 3 + 3 = 14 meters.
Perpendicular bisector theorem
The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a given circle with straightedge and compass.
Scale factor
The ratio of any two corresponding lengths in two similar geometric figures. Note: The ratio of areas of two similar figures is the square of the scale factor. The ratio of volumes of two similar figures is the cube of the scale factor.
Area
The size of a surface. The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle or circle. These shapes all have the same area of 9. Help me find how many square meters. Drag the squares to measure it.
Base of an isosceles triangle
The unequal side of an isosceles triangle is usually referred to as the 'base' of the triangle. ... When the 3rd angle is a right angle, it is called a "right isosceles triangle". The altitude is a perpendicular distance from the base to the topmost vertex.
Side-splitter theorem
Topical Outline | Geometry Outline | MathBits' Teacher Resources. Terms of Use Contact Person: Donna Roberts. The "Side Splitter" Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally.
Similar figure
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. ... Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure.
Congruent polygons
Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal. Move your mouse cursor over the parts of each figure on the left to see the corresponding parts of the congruent figure on the right.