Grade 7 Geometry Quiz

Geometry comes from the two Greek words geo and metron which mean 'Earth' and 'to measure'. This suggests that geometry is the branch of mathematics that deals with the measurement and properties of shapes, figures, and spaces. It involves studying the relationships and properties of points, lines, angles, surfaces, and solids.

Parallel lines are lines that are always the same distance apart and never intersect. They continue indefinitely in the same direction, never meeting or crossing each other. This is why they are described as going on forever but never meeting.

The guitar string is an example of a line because it is a long, thin object that extends indefinitely in both directions. It has one dimension, length, and does not have any width or depth. The guitar string can be represented mathematically as a straight line, and it is often used to produce musical notes by vibrating in a linear fashion.

The degree of a straight line is 180° because a straight line forms a straight angle, which is a line that measures 180°. In geometry, a straight line is the shortest distance between two points and it does not bend or curve. Therefore, the angle formed by a straight line is always 180°.

An obtuse angle is a type of angle that measures between 90 and 180 degrees. It is larger than a right angle (90 degrees) but smaller than a straight angle (180 degrees).

A point in a plane can have an infinite number of lines going through it because there are an infinite number of possible directions in which a line can be drawn in a plane. Regardless of the position or orientation of the point, there will always be an infinite number of lines that can pass through it.

The given options are all possible ways to name an angle formed by three points A, B, and C, except for "angle BAC". This is because when naming an angle, the vertex (in this case, point A) should always be in the middle. The correct way to name the angle formed by points A, B, and C is "angle ABC".

Supplementary angles are two angles that add up to 180 degrees. To find the supplementary angle of a given angle, you subtract the given angle from 180 degrees. In this case, 180 degrees - 22 degrees = 158 degrees. Therefore, the supplementary angle of 22 degrees is 158 degrees.

The complementary angle of 46° is 44°. Complementary angles are two angles that add up to 90°. To find the complementary angle, you subtract the given angle from 90°. In this case, 90° - 46° equals 44°. This means that 44° is the angle that, when added to 46°, gives a total of 90°. This concept is fundamental in geometry, particularly in problems involving right angles. ​​

In the given figure,

The sum of the three angles inside the triangle is 180°.

The third angle will then be = 180 - 58 - 68 = 54°.

Now, x + 54° = 180°

x = 126°

Therefore, the missing angle would be 126°.

In the given figure, Line PAQ is a tangent. A tangent is a line that touches a curve at only one point and is perpendicular to the radius at that point. In this case, line PAQ touches the curve at point A and is perpendicular to the radius at that point. Therefore, it can be concluded that line PAQ is a tangent.

An angle bisector is a segment that divides any angle of a triangle into two angles of equal measures. It is a line that cuts an angle in half, creating two smaller angles that have the same measure. In the context of a triangle, an angle bisector starts from a vertex and divides the opposite side into two segments that are proportional to the adjacent sides.

In the given figure, line DE intersects the circle at two points, creating a segment within the circle. This segment is known as a chord. Therefore, the correct answer is chord.

Alternate interior angles are a pair of angles formed when a transversal intersects two parallel lines. In the given figure,

A segment is not an Undefined Term because it has a specific definition in geometry. A segment is a part of a line that consists of two endpoints and all the points between them. In contrast, a point, line, and plane are all examples of Undefined Terms in geometry because they are basic concepts that are not defined or explained further.

The statement "all squares are rectangles" is correct because a square is a special type of rectangle. A rectangle is defined as a quadrilateral with four right angles, and a square meets this definition as it has four right angles. Additionally, a square also has the additional property of having all sides equal in length, which makes it a special case of a rectangle. Therefore, all squares can be classified as rectangles, but not all rectangles can be classified as squares.

The points A, B, and C are coplanar because they all lie on the same plane. A plane is a two-dimensional flat surface that extends infinitely in all directions. Therefore, if three points lie on the same plane, they are coplanar.

Two distinct rays sharing the same vertex and lying on the same line are known as "opposite rays" or "opposite vectors." These rays extend indefinitely in opposite directions from the common endpoint, forming a straight line.

When two planes intersect, they form a line. This is because a plane is a two-dimensional surface, and when two planes intersect, they create a common boundary or edge, which is a one-dimensional object known as a line. Therefore, the correct answer is "Line."