Geometry

In a triangle, the sum of all three angles is always 180 degrees. If two angles add up to 108 degrees, you can find the third angle by subtracting that sum from 180 degrees: 180 - 108 = 72 degrees. Therefore, the third angle measures 72 degrees.

No, a pair of angles cannot be both vertical and complementary at the same time. Vertical angles are formed by the intersection of two lines and are always equal in measure. Complementary angles, on the other hand, are two angles whose measures add up to 90 degrees. Since vertical angles are equal, they would only be complementary if each angle measures 45 degrees, which is not generally the case.

YES!!!

Polygons are all 2-dimensional shapes.

Compare to

Polyhedrons are all 3-dimensional solids.

'poly' means ; Many

'gons' 2-dimensional

'hedrons 3-dimensional

So a polygon is a 2-dimensional shape of any number of sides.

A polyhedron is a 3-dimensional solid of any number of faces.

There are three types of shapes.

#1 ; 1-dimensional ; a straight line

#2 ; 2-dimensional ; a figures drawn in two dimension, such as a circle.

#3 ; 3-dimensional ; a solid exists in 3 dimension, such a sphere.

Geometry.

I think of it as PICTORIAL Mathematics.

The word 'geometry' comes from Classical Greece, and means ' Measuring the World'.

NB

Geo ; the world

Metry ; to measure.

Also very critical geometric shape are PARALLEL Lines. They only meet at INFINITY.

Base length X PERPENDICULAR height..

NOT the sloping height.

Being a parallelogram draw a right-angled line from the base line to 'top' parallel line. ; this is the PERPENDICULAR Height.

To find the altitude of the plane after it has traveled 10 kilometers horizontally, we can use trigonometry. The altitude (h) can be calculated using the sine function: ( h = d \cdot \tan(\theta) ), where ( d ) is the horizontal distance (10 km) and ( \theta ) is the angle of ascent (15 degrees). Therefore, ( h = 10 \cdot \tan(15^\circ) ), which gives an altitude of approximately 2.6 kilometers.

No, the graphs of two different direct variations cannot be parallel. Direct variation is represented by the equation ( y = kx ), where ( k ) is the constant of variation. For two direct variations to be parallel, they would need to have the same slope, which means they would have the same value of ( k ). However, since the variations are different, they must have different values of ( k ), resulting in non-parallel graphs.

To rotate a figure 270 degrees counterclockwise about the origin, you can achieve this by rotating it 90 degrees clockwise, as 270 degrees counterclockwise is equivalent to 90 degrees clockwise. For each point (x, y) of the figure, the new coordinates after the rotation will be (y, -x). This transformation effectively shifts the figure to its new orientation while maintaining its shape and size.

The electron geometry for carbon disulfide (CS2) is linear. In CS2, the central carbon atom is bonded to two sulfur atoms with double bonds, resulting in a total of two regions of electron density around the carbon. This arrangement leads to a linear shape, with a bond angle of approximately 180 degrees.

A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface at a fixed distance from the center. The axis of the cylinder is the line segment that joins the centers of the two bases, and it is perpendicular to the bases. Cylinders can be classified as right cylinders, where the sides are perpendicular to the bases, or oblique cylinders, where the sides are slanted. Common examples include cans and tubes.

The pause button is represented by two vertical lines to symbolize the interruption of a continuous action, such as playback. This design intuitively conveys the idea of halting the flow of media, making it easily recognizable across various devices. The two lines create a visual balance and clarity, distinguishing the pause function from other controls like play or stop. This simple yet effective design has become a universal icon in media controls.

The Malaysian ringgit is often abbreviated as MYR, which stands for Malaysian Ringgit. In addition, it is sometimes referred to as "ringgit" alone, as the term means "jagged" in Malay, originally describing the Spanish dollar's serrated edges. Some informal references may include "bucks" in casual conversation.

In the construction of an equilateral triangle, you can prove that segments AB and BC are congruent by using the fact that all sides of an equilateral triangle are equal by definition. Additionally, when constructing the triangle using a compass, the same radius is used to create the arcs that define points B and C from point A, ensuring that AB = AC = BC. Thus, by the definition of an equilateral triangle and the properties of congruent segments created during the construction, AB and BC are congruent.

The dimensions provided (4 cm, 2 cm, and 1 cm) do not form a cube; they represent a rectangular prism instead. The volume of a rectangular prism is calculated by multiplying its length, width, and height. Therefore, the volume is 4 cm × 2 cm × 1 cm, which equals 8 cubic centimeters (cm³).

A trapezium (or trapezoid in some regions) does not necessarily have three equal angles. In fact, a trapezium typically has only two pairs of angles, with one pair being equal (the angles adjacent to each base). For a trapezium to have three equal angles, it would have to be a specific type of trapezium with particular angle measures, which is not common. Thus, in general, a trapezium does not have three equal angles.

To determine if you can pour 120 cm of liquid into the vase, you need to calculate the vase's volume. The volume of the vase is height × width × length, which equals 4 cm × 4 cm × 5 cm = 80 cm³. Since 120 cm exceeds the vase's capacity of 80 cm³, you cannot pour that amount into the vase without overflowing.

The radius of the largest sphere that can fit entirely inside a rectangular box is determined by the smallest dimension of the box. In this case, the dimensions of the box are 4 cm, 6 cm, and 10 cm, with 4 cm being the smallest. Therefore, the radius of the largest sphere that can fit inside the box is half of the smallest dimension, which is 2 cm.

The number of words on a line can vary significantly depending on factors such as the font size, typeface, and the width of the text container. In standard formatting, a typical line of text may contain about 8 to 12 words. However, this can change with different layouts and design choices. For precise measurements, it’s best to refer to specific formatting guidelines or tools.

A delta, or equilateral triangle, has 3 rotational symmetries. These occur at rotations of 0 degrees (the original position), 120 degrees, and 240 degrees. Each rotation aligns the triangle with its original shape, demonstrating its symmetry.

To find the perimeter of a triangle, you add the lengths of all its sides. For a triangle with sides measuring 8 cm, 6 cm, and 1 cm, the perimeter is calculated as follows: 8 cm + 6 cm + 1 cm = 15 cm. Therefore, the perimeter of the triangle is 15 cm.

Not all polygons have point symmetry. A polygon exhibits point symmetry if for every point in the shape, there is another point at an equal distance in the opposite direction from a central point. Regular polygons, like squares or equilateral triangles, possess point symmetry, but irregular polygons may not. Thus, only certain types of polygons, particularly regular ones, can be said to have point symmetry.

True. To begin an indirect proof, you assume the opposite (or inverse) of what you intend to prove is true. This assumption leads to a contradiction, thereby demonstrating that the original statement must be true.

A cube has 6 faces, 12 edges, and 8 vertices. Each face of the cube is a square, and it is formed where the edges meet. The edges connect the vertices, which are the points where the corners of the cube meet.