WorksheetsPlane & Solid Geometry
Total questions: 102
Worksheet time: 51mins
An annulus is a plane figure which is composed of two concentric circles. The area of the annulus can be calculated by getting the difference between the area of the larger cirde and the area of the smaller circle. Also, its area can be calculated by removing the hole. This method is called
Law of extremities
Law of reduction
Law of deduction
Sharp theorem
Each of the faces of a regular hexahedron is a
Square
Triangle
Rectangle
Hexagon
It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are parallelograms
Tetrahedron
Prism
Frustum
Prismatoid
The apothem of a polygon is ____ of its inscribed circle
Radius
Circumference
Diameter
Length
Each angle of regular dodecagon is equal to
135
150
125
105
The area bounded by two concentric circles is called
Ring
Disk
Annulus
Sector
One-fourth of a great circle is called
Cone
Sector
Quadrant
Arc
Points that lie on the same plane are called
Coplanar
Parallel
Collinear
Oblique
The volume of a circular cylinder is equal to the product of its base and altitude
Axiom
Postulate
Theorem
Corollary
The study of properties of figures in three dimensions
Physics
Plane trigonometry
Solid geometry
Trigonometry
A plane closed curve, all points of which are the same distance from a point within, called center.
Polyhedron
Polygon
Circle
Ellipse
What is the angle of π and less than 2π?
Straight line
Obtuse angle
Oblique angle
Acute angle
What is the value in degrees of 1 radian?
90°
57.3°
60°
33°
Prisms are named according to their ____
Diagonals
Sides
Vertices
Bases
In plane geometry, two circular arcs that together make up a full circle are called
Coterminal arcs
Conjugate arcs
Congruent arcs
Half arcs
Polygons are classified according to the number of ____
Vertices
Sides
Diagonals
Angles
When two planes intersects with each other, the amount of divergence between the two planes in expressed by measuring the
Dihedral angle
Plane angle
Polyhedral angle
Reflex angle
An angular unit equivalent to 1/4000 of the circumference of a circle is called
Mil
Degree
Radian
Grad
Express 45° in mils
80
800
1600
2700
The arc length equal to the radius of the circle is called
Radian
Quarter sector
Sector
Semicircle
A five-pointed star is also known as
Pentagon
Pentatron
Pentagram
Quintagram
If two or more lines have a single point which lies on all of them, then they are
Collinear
Coplanar
Concurrent
Conjugate
The action of bringing one geometric figure into coincidence with another is called
Transposition
Translation
Superposition
Projection
A line that intersect two or more lines at distinct points
Tangent line
Transversal
Bisector
Median
An arc length equal to the radius of a circle
Grad
Radian
Degree
Mil
An angle which is 1/400th of the full revolution
Gon
Mil
Degree
Radian
Another term for gon
Grad
Mil
Centesimal degree
A and C
An angle whose vertex is a point on the circle and whose sides are chords in known as
Interior angle
Vertical angle
Actue angle
Inscribed angle
An angle greater than the right angle but less than a straight angle
Acute angle
Obtuse angle
Reflex angle
Oblique angle
Any angle greater than a straight angle but less than two straight angles is known as ____ angle
Compliment
Supplement
Complex
Reflex
The angle formed by the prolongation of one side and the adjacent side of the polygon.
Interior angle
Acute angle
Exterior angle
Explementary angle
Two angles which have the same vertex and the sides of one are form by extending the sides of the other
Adjacent angles
Vertical angles
Deflection angles
Another term for exterior angle
Vertical angle
Inscribed angle
Reflex angle
Deflection angle
What is the sum of all deflection angles in given polygon?
Always less than 360°
Always equal to 360°
Always greater than 360°
Always equal to 180°
The coterminal angle of 120° is
240°
-240°
480°
-480°
Two planes intersect each other. What is the term for the angle formed perpendicular to the intersection of two planes?
Solid angle
Plane angle
Base angle
Dihedral angle
When a terminal side of an angle coincides with an axis, the angle is a
Coterminal angle
Right angle
Quandrantal angle
Reflex angle
If the exterior angle of a polygon is obtuse, its corresponding interior angle is
An acute angle
Also an obtuse angle
A reflex angle
Always greater than 160°
The measure of 2.25 revolutions counterclockwise is
835°
805°
810°
815°
Solid angles are measured in
Mil
Radians
Steradians
Circular mils
What is the largest measure (in steradians) of the solid angle?
2π
4π
8π
π
Steradians measure in space in analog of ____ measured in the plane
Radians
Degrees
Mils
Grads
A part of a circle called
Sector
Segment
Chord
Arc
It is a union of the chord of a circle and the intercepted arc
Sector
Segment
Lune
Zone
A _____ of a circle in the figure bounded by two radii and the intercepted arc
Major arc
Minor arc
Segment
Sector
As the area of the circle increases, the ratio of its circumference to its diameter
Increases
Remains constant
Decreases
Will be equal to 1
A circle is said to be _____ to a polygon having the same perimeter with that of the circle
Congruent
Isoperimetric
Proportional
Convex
Which of the following is NOT a property of a circle?
Through 3 points not in a straight line, only one circle can be drawn
A tangent to a circle is perpendicular to the radius at the point of tangency and conversely
An inscribed angle is measured by one half of the intercepted arc.
The arcs of two circles subtended by equal central angles are always equal
All circles having the same center but of unequal radii are called
Concentric circles
Eccentric circles
Inner circles
Pythagorean circles
Two chords of a circle which joins a point on the circle to the end points of a diameter and forms a right angle
Complementary chords
Supplementary chords
Focal chords
Chords of contrast
The center of the inscribed circle of a triangle is known as ____ of the triangle
Circumcenter
Incenter
Excenter
Orthocenter
Supplementary chords are two chords which join a point on the circle to the endpoirts of a diameter. The supplemental chords subtend a/an ____ angle.
Acute
Right
Obtuse
Reflex
A circle or radius R has a curvature of
R2
1/R
2R
√R
A polygon is ____ when no side, when extended, will pass through the interior of the polygon
Convex
Equilateral
Isoperimetric
Similar
A polygon is said to be regular polygon if its is
Convex
All sides are congruent
All angles are congruent
All of the above
Polygon inscribed in the same circle called
Concentric polygons
Ocentric polygons
Concylic polygons
Orthocentric polygons
If n is the number of sides of a polygon, then the sum of all interior angles of a polygon is expressed as
(n+2) 180°
(n/2) 180°
(n-2) 180°
(n/2)(n-3)
If n is the number of sides of a polygon, then the number of diagonals of a polygon is expressed as
n!
(n-1)!
(n/2)(n-3)
(n/3)(n-2)
What do you call a polygon with 11 sides?
Unagon
Unogon
Undecagon
Dodecagon
Pentagon is to 5 sides as ____ is to 11 sides
Heptagon
Septagon
Unidecagon
Hendecagon
A polygon having 12 sides is called
Bidecagon
Dodecagon
Nonagon
Pentedecagon
A polygon of 100 sides is called
Chilliagon
Ennagon
Perigon
Milliagon
The highest point of a figure relative to a baseline or plane is called
Summit
Highest ordinate
Terminal point
Indicate the false statement
A trapezoid is a quadrilateral two and only two of whose sides are parallel.
The sum of two sides of a triangle is greater than the third side and their difference is less than the third side.
A diagonal of a polygon is a iine joining any-non-consecutive vertices.
Two angles are complementary if their sum is equal to 180°
Which of the following statements is correct?
All right-angled triangles are similar
All isosceles triangles are similar
All equilateral triangles are similar
All rectangles are similar
A quadrilateral with no sides parallel.
Trapezoid
Rhombus
Rhomboid
Trapezium
Which of the following BEST describes Ptolemy's theorem?
It is use only for quadrilaterals
It is just a modification of Brahmagupta's theorem
It is used only for cyclic quadrilaterals
The sum of the square of the sides is equals to the square of the diagonals of a guven quadrilateral
The five-pointed star described by the diagonals of a regular Pentagon
Perigon
Pentegram
Penacle
Pentegram or penacle
The geometric figure remaining after a parallelogram has been removed from one corner of a larger similar polygon.
Gnomon
Gaussian plane
Lozenge
An oblique-angled parallelogram with four sides equal is called
Rhombus
Diamond
Lozenge
All of the above
A non-convex quadrilateral with two pairs of adjacent equal sides is called
Trapezium
Kite
Deltroid
Diamond
What is another term for a parallelogram?
Rectangle
Quadrangle
Diamond
Rhomboid
A solid cut of a given solid by two non parallel planes is called
Frustum
Prism
Truncated prism
Prismatoid
A polyhedron having bases two polygons in parallel planes and for lateral faces triangles or trapezoids with one side lying on the other base of the polyhedron
Pyramid
Cone
Prismatoid
Truncated prism
Portion of regular solid left after cutting off the upper part by a plane parallel to the base
Frustum
Ungula
Truncated solid
Prismatoid
Body of space bounded by surface every point of which is equidistant from a point within
Circle
Sphere
Spheroid
Ellipsoid
A solid bounded by a zone and the planes of the zone's base
Spherical sector
Spherical segment
Lune
Spherical excess
The intersection of the sphere and the plane through the center is called
Great circle
Small circle
Poles
Polar distance
The portion of a sphere enclosed between two great semi circles having common end points including the semi circle
Spherical excess
Spherical segment
Zone
Lune
A portion of the surface of a sphere including between two parallel planes
Spherical excess
Spherical segment
Zone
Lune
If R is the radius of the sphere and h s the distance between two parallel plane the area of the zone is
2πRh
4πRh
πh²(3R - h)/3
4π(R - h)
The solid bounded by two great circles and the surface of a sphere is known as
Spherical zone
Spherical segment
Spherical cone
Spherical wedge
A cone or cylinder with its top cut off by plane oblique to the base
Frustum
Prismoid
Prismatoid
Ungula
A term given to cylinder with elliptical cross section
Cylindroid
Cylindoid
Ovaloid
Deltroid
A doughnut-like surface of revolution generated by rotating the circle through 360° in space about a line in its plane but now passing through the circle
Torus
Annulus
Anchor
All of the above
A regular solid star in a shape that is radiating from center like rays of star
Pentagram
Pentagon
Stellated solid
Archimedean solid
Formed by intersection of rays from one point reflected of refracted from a curvature surface
Envelop
Caustic
Evolute
Pencil
There regular polyhedron is a solid with all its faces identical regular polygons. The regular polyhedrons are knows as
Euclidean solids
Pythagorean solids
Platonic solids
Newtonian solids
There are how many regular polyhedra known to man
5
3
7
10
An icosahedron is a regular polyhedron of _____ faces
12
14
16
20
A regular polyhedron with 6 sides is called
Dodecahedron
Hexahedron
Tetrahedron
Octahedron
The face of a regular tetrahedron is a
Square
Pentagon
Hexagon
Triangle
The face of a regular octahedron is a
Square
Pentagon
Hexagon
Triangle
The face of a regular dodecahedron is a
Square
Pentagon
Hexagon
Triangle
The face of a regular icosahedron is a
Square
Pentagon
Hexagon
Triangle
Which regular polyhedron does not have a face a triangle
Tetrahedron
Octahedron
Icosahedron
Dodecahedron
How many edges are there in a dodecagon
6
12
30
8
A tetrahedron has ____ vertices
4
3
6
5
Given two solids and a plane. Supposed that every plane parallel to the given plane intersecting one of the two solids, also intersects the other and given cross-sections with the same area then the two solids have the same volume. This is known as the
Unit postulate
Plane postulate
Parallel postulate
Cavallieri`s postulate
Who formulated the cavalieri`s principle
Harold cavalieri
Buenaventura cavalieri
Joefry cavalieri
Carl cabalieri
A line segment that is divided into two segments a greater a and a smaller b such that the length of a + b is to a and a is to b. Such division is known as
Golden segment
Golden ratio
Golden proportion
All of the above
The volume of a paraboid is equal to ____ the volume o circumscribing cylinder
1/3
1/2
1/4
2/3
