Term
In the image below, if the horizontal lines are parallel, which angle is congruent with ∠1? [image] 

Definition
Angle 1 has three congruent angles: ∠4, ∠5, and ∠8. 


Term
In the image below, if the horizontal lines are parallel, which angle is congruent with ∠2?
[image] 

Definition
Angle 2 has three congruent angles: ∠3, ∠6, and ∠7. 


Term
In Geometry, How Big is a Point? 

Definition


Term
In Geometry, What is a Line? 

Definition
A straight line that extends in both directions without end. 


Term
In Geometry, What is a Plane? 

Definition
A flat, twodimensional surface that extends in every direction without end. It can be thought of as a floor which has no thickness and that extends infinitely far in all directions. 


Term

Definition
The part of a line between two points. It contains those points and all of the points between them. 


Term

Definition
The points at each end of a line segment. 


Term

Definition
Line segments that have equal length. 


Term

Definition
The point that divides a line segment into two congruent line segments. 


Term
If You Have a Given Line with Points A, B, C, and D on it, What is AB Used to Denote? 

Definition
It can denote one of two things: 1) The line segment that consists of points A and B as well as all points between them. 2) The length of the line segment AB. You can determine the meaning from the context. 


Term
Fill in the Blank: When Two Lines Intersect at a Point, They Form Four ________. 

Definition


Term
Fill in the Blank: When Two Lines Intersect at a Point, They Form ______ Angles. 

Definition


Term
Fill in the Blank: When Two Lines Intersect at a Point, Each Angle has a ______ at the Point of Intersection. 

Definition


Term
Fill in the Blank: When Two Lines Intersect at a Point, Each Angle has a Vertex at the ______. 

Definition


Term
Fill in the Blank: When Two Lines Intersect at a Point, Each ______ has a Vertex at the Point of Intersection. 

Definition


Term
If Line Segment AB Intersects Line Segment CD at Point P, What are Angles APC and BPD Called? 

Definition
Opposite angles, or vertical angles. 


Term
If Line Segment AB Intersects Line Segment CD at Point P, What is the Sum of the Measures of All Four Angles Produced? 

Definition


Term
If Line Segment AB Intersects Line Segment CD at Point P, Which Angles are Opposite? 

Definition
There are two pairs of opposite angles: APC and BPD. APD and CPB. 


Term
If Line Segment AB Intersects Line Segment CD at Point P, Which Angles are Vertical? 

Definition
There are two pairs of vertical angles: APC and BPD. APD and CPB. 


Term
If Line Segment AB Intersects Line Segment CD at Point P, Which Angles are Congruent? 

Definition
There are two pairs of congruent angles: APC and BPD. APD and CPB. 


Term

Definition
When two lines or line segments intersect, the opposite angles are the angles opposite one another. If line segment AB intersects line segment CD at point P, it will have two pairs of opposite angles: APC and BPD. APD and CPB. Opposite angles are always congruent. 


Term

Definition
When two lines or line segments intersect, the vertical angles are the angles opposite one another. If line segment AB intersects line segment CD at point P, it will have two pairs of vertical angles: APC and BPD. APD and CPB. Vertical angles are always congruent. 


Term

Definition
Angles that have equal measures. 


Term
Fill in the Blank: Opposite Angles Have ______ Measures. 

Definition


Term
In Geometry, What Does the ∠ Symbol Mean? 

Definition


Term

Definition
Lines that intersect to form four congruent angles of 90ᵒ each. 


Term
In Geometry, What Does the ⊥ Symbol Mean? 

Definition
Perpendicular. Two lines that are perpendicular are denoted by a⊥b. 


Term

Definition
An angle with a measure of 90ᵒ. 


Term
What Does it Mean When a Small Square is Drawn at the Vertex of an Angle? 

Definition
It is a right angle (its measure is 90ᵒ). 


Term
Fill in the Blank: You Can Denote a Right Angle by Drawing a Small ______ at the Vertex of the Angle. 

Definition


Term

Definition
An angle with a measure less than 90ᵒ. 


Term

Definition
An angle with a measure between 90ᵒ and 180ᵒ. 


Term

Definition
Two lines on the same plane that do not intersect. 


Term
If Two Parallel Lines are Intersected by a Third Line, What Do You Know About the Angles? 

Definition
Four of the angles will be congruent to one another, the other four will be congruent to each other. That is to say, there will be two measures, each of which is shared by two angles. The only exception is if the intersecting line is perpendicular to the parallel ones, in which case all 8 angles will be 90ᵒ. 


Term

Definition
A closed figure formed by three or more line segments which join the others at their endpoints. Each of the line segments is called a side. 


Term
In Geometry, What is a Side? 

Definition
Each of the line segments that make up a polygon is called a side. 


Term

Definition
The endpoints where each line segment joins with the endpoints of another in a polygon. 


Term

Definition
A polygon in which the measure of each interior angle is less than 180ᵒ. 


Term

Definition
A polygon with three sides. 


Term

Definition
A polygon with four sides. 


Term

Definition
A polygon with five sides. 


Term
Fill in the Blank: A Quadrilateral Can Be Divided into ______ Triangles. 

Definition


Term
Fill in the Blank: A Pentagon Can Be Divided into ______ Triangles. 

Definition


Term
How Many Triangles can a Polygon be Divided Into? 

Definition
It can be divided into n2 triangles, where n is the number of sides the polygon has. 


Term
What is the Sum of the Measures of the Interior Angles of a Polygon? 

Definition
(n2)(180ᵒ), where n is the number of sides the polygon has. 


Term
What is the Sum of the Measures of the Interior Angles of a Quadrilateral? 

Definition
(n2)(180ᵒ) = (42)(180ᵒ) = (2)(180ᵒ) = 360ᵒ 


Term

Definition
A polygon with six sides. 


Term

Definition
A polygon with eight sides. 


Term

Definition
A polygon in which all sides are congruent and all interior angles are congruent. 


Term
What is Another Name for a Regular Quadrilateral? 

Definition


Term
How Do You Calculate an Interior Angle for a Regular Polygon? 

Definition
Divide the sum of the measures of the interior angles by the numer of sides the polygon has. [(n2)(180ᵒ)]/n 


Term
What is the Measure of Each Angle in a Regular Hexagon? 

Definition
[({6}2)(180ᵒ)]/(6) [(4)(180ᵒ)]/6 720ᵒ/6 120ᵒ Each angle will be 120ᵒ. 


Term

Definition
The sum of the lengths of all of its sides. 


Term

Definition
The area of the region enclosed by a polygon. 


Term
What is Special About the Lengths Each Side of a Triangle? 

Definition
The length of each side must be less than the sum of the other two sides. 


Term
If a Triangle has One Side with a Length of 3 and Another with a Length of 14, What are the Minimum and Maximum Values for the Remaining Side? 

Definition
x < 3+14 x < 17 AND: x > 143 x > 11 The remaining side must be between 11 and 17. This can be denoted as 11 < x < 17. 


Term

Definition
A triangle with three congruent sides. The measure of each angle is 60ᵒ. All equilateral triangles are also isosceles triangles. 


Term
What is Another Name for a Regular Triangle? 

Definition


Term

Definition
A triangle with at least two congruent sides. The angles opposite the congruent sides (the angles which are NOT at the intersection of the two sides) will also be congruent. 


Term
In Triangle ABC, if AB and BC are Congruent, Which Angles are Congruent? 

Definition


Term
In Triangle ABC, if ∠A and ∠C are Congruent, Which Sides are Congruent? 

Definition


Term

Definition
A triangle with an interior right angle (an interior angle equal to 90ᵒ). 


Term

Definition
The side opposite the right angle in a right triangle. 


Term

Definition
The sides of a right triangle other than the hypotenuse. If triangle ABC has a 90ᵒ angle at B, the hypotenuse will be AC, and the legs will be AB and BC. 


Term

Definition
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 legs. a²+b² = c² If triangle ABC has a 90ᵒ angle at B, this would be denoted by: (AB)²+(BC)² = (AC)² 


Term
In a Right Triangle, if the Length of One Leg is 6 and the Length of the Other Leg is 8, What is the Hypotenuse? 

Definition
(6)²+(8)² = c² 36+64 = c² 100 = c² c = √100 = 10 The hypotenuse is 10. 


Term
In a Right Triangle, if the Length of One Leg is 4 and the Length of the Hypotenuse is 7, What is the Length of the Remaining Leg? 

Definition
(4)²+b² = (7)² 16+b² = 49 b² = 4916 = 33 b = √33 The remaining leg is √33, or approximately 5.74. 


Term
What is the Equation Used to Determine the Length of the Sides for an Isosceles Right Triangle? 

Definition


Term
What is the Ratio for the Lengths of the Sides for an Isosceles Right Triangle? 

Definition


Term
What are the Values of the Angles for an Isosceles Right Triangle? 

Definition
One angle is 90ᵒ and the other two are each 45ᵒ. 


Term

Definition
A right triangle where the value for one of the remaining angles is 30ᵒ and the value for the third angle is 60ᵒ. It is half of an equilateral triangle. 


Term
A ______ is Half of an Equilateral Triangle. 

Definition


Term
What is the Ratio for the Lengths of the Sides for a 30ᵒ60ᵒ90ᵒ Triangle? 

Definition


Term
What is the Equation Used to Determine the Length of the Sides for a 30ᵒ60ᵒ90ᵒ Triangle? 

Definition
y = (√3)x Where y is the side opposite the 60ᵒ angle, x is the side opposite the 30ᵒ angle. The hypotenuse is 2x. The side x will be shorter than the side y. 


Term
How Do You Calculate the Area of a Triangle? 

Definition
Multiply the base by the height and divide by 2. A = bh/2 


Term
Which Side of a Triangle is the Base? 

Definition
Any side can be the base. The height is the perpendicular line segment from the base to the opposite vertex. 


Term
Which Side of a Triangle is the Height? 

Definition
The perpendicular line segment from the base to the opposite vertex. 


Term

Definition
Two triangles that have the same shape and size. Two triangles are congruent if their vertices can be matched up so that the corresponding angles and the corresponding sides are congruent. All congruent triangles are also similar. 


Term
How Do You Determine if Two Triangles are Congruent? 

Definition
There are three ways: 1) If all three sides of one triangle are congruent to all three sides of another triangle, they are congruent. 2) If two sides and one angle of one triangle are congruent to two sides and one angle of the other triangle, they are congruent. 3) If two angles and one side of one triangle are congruent to two angles and one side of the other triangle, they are congruent. 


Term
If All Three Angles of a Triangle are Congruent, Does That Mean the Triangles are Congruent? 

Definition
No. They are only similar. 


Term
If All Three Sides of a Triangle are Congruent, Does That Mean the Triangles are Congruent? 

Definition


Term
If Two Sides and One Angle of a Triangle are Congruent to Two Sides and One Angle of Another Triangle, What Do You Know? 

Definition
The triangles are congruent. 


Term
If Two Angles and One Side of a Triangle are Congruent to Two Angles and One Side of Another Triangle, What Do You Know? 

Definition
The triangles are congruent. 


Term

Definition
Two triangles that have the same shape but not necessarily the same size. When talking about simlilar triangles ABC and DEF, the order of the letters indicates their correspondences. The ratio of their sides will also be equal to one another. 


Term
If Triangles ABC and DEF are Similar, Which Angles are Congruent? 

Definition
∠A is congruent to ∠D, ∠B is congruent to ∠E, and ∠C is congruent to ∠F. 


Term
If Triangles ABC and DEF are Similar, What Do You Know About the Ratios of Their Sides? 

Definition
AB/DE = BC/EF = AC/DF You can also use crossmultiplication to get: AB/BC = DE/EF AB/DE = AC/DF AC/BC = DF/EF 


Term
If You Have Two Triangles, ABC and DEF, and You Know that AB/DE = BC/EF = AC/DF, What Can You Conclude? 

Definition
They are similar triangles. 


Term

Definition
A quadrilateral with four right angles. 


Term

Definition
A rectangle with four congruent sides. A regular quadrilateral. 


Term

Definition
A quadrilateral in which both pairs of opposite sides are parallel. Both pairs of opposite sides and opposite angles are congruent. 


Term
Fill in the Blank: In a Parallelogram Both Pairs of ______ are Congruent. 

Definition
Opposite sides AND opposite angles. 


Term

Definition
A quadrilateral in which two opposite sides are parallel. 


Term
How Do You Calculate the Area of a Parallelogram? 

Definition
A = bh, where b is the base and h is the height. 


Term
When Calculating the Area of a Parallelogram, Which Side is the Base? 

Definition
Any side may be the base. 


Term
When Calculating the Area of a Parallelogram, What is the Height? 

Definition
The height is the perpendicular line segment from any point on the base to the opposite side (or an extension of that side). 


Term
How Do You Calculate the Area of a Trapezoid? 

Definition
A = (1/2)(b₁+b₂)(h), where b₁ is the length of one parallel side, b₂ is the length of the other parallel side, and h is the corresponding height (the perpendicular line segment between the parallel sides). In English: The area equals half of the product the height and the sum of the lengths of the two parallel sides. 


Term

Definition
The sum of all of the sides of a polygon. 


Term

Definition
The set of points on a plane that are a distance of r units from O, where r is a positive number and O is a point on the plane. 


Term

Definition
The point O on a plane (where the circle is defined as the set of points on a plane that are a distance of r units from O, and r is a positive number). 


Term

Definition
The distance from the center of a circle to its edge. Any line segment joining a point on the circle and the center of that circle. 


Term

Definition
The plural form of radius. 


Term

Definition
Twice the radius. Any chord which passes through the center of that circle. 


Term

Definition
Any line segment joining two points on a circle. 


Term

Definition
The distance around a circle, analogous to the perimeter of a polygon. 


Term
What is the Ratio for Pi? 

Definition
C/d, where C is the circumference of any circle and d is the diameter of the 


Term
What is the Approximate Value of Pi (Don't Use a Calculator for This)? 

Definition


Term
What is the Symbol π Used to Denote? 

Definition
Pi, which has an approximate value of 3.14, and is the ratio of C/d. 


Term
How Do You Calculate the Circumference of a Circle? 

Definition
C = 2πr, where r is the radius. 


Term
If a Circle has a Diameter of 12, What is the Circumference? 

Definition
The radius if half of the diameter, so: C = 2π(1/2)(12) = 37.6991 Which can be rounded to 37.7. 


Term

Definition
The part of the circle containing two points and all the points between them. Two points on a circle are always the endpoints of TWO arcs. 


Term
How Many Points are Used to Identify an Arc? 

Definition
Arcs are identified by three points. This is to avoid ambiguity, as two points would refer to two arcs instead of one. 


Term

Definition
An angle with its vertex at the center of the circle. 


Term

Definition
The measure of its central angle, which is formed by two radii that connect the center of the circle to the endpoints of the arc. 


Term
Fill in the Blank: An Entire Circle is Considered to be an ______ with Measure 360ᵒ. 

Definition


Term
If You Know the Measure of an Arc Formed by Two Points, What Do You Know About the Other Arc Formed by Those Same Two Points? 

Definition
It will be equivalent to 360ᵒa, where a is the measure of the first (known) arc. 


Term

Definition
The distance around the circumference of the circle from one endpoint of the arc to the other. 


Term
What is the Ratio for the Circumference of an Arc? 

Definition
The ratio of the length of an arc to the circumference is equal to the ratio of the degree measure of the arc to 360ᵒ. a/C = ∠b/360 Where a is the length of the arc, C is the circumference of the circle, and ∠b is the measure of the arc. 


Term
How Do You Calculate the Length of an Arc? 

Definition
a = C(∠b/360) Where a is the length of the arc, C is the circumference of the circle, and ∠b is the measure of the arc. 


Term
If the Radius of a Circle is 6 and the Measure of an Arc is 45ᵒ, What is the Length of the Arc? 

Definition
a = C(45/360) We know that C = 2π(6) = 12π, so: a = 12π(45/360) = 12π(0.125) = 1.5π The length is 1.5π or approximately 4.71. 


Term

Definition
The area of the region enclosed by a circle. 


Term
How Do You Calculate the Area of a Circle? 

Definition
A = πr², where r is the radius. 


Term
If a Circle has a Diameter of 12, What is the Area? 

Definition
The radius if half of the diameter, so: C = π[(1/2)(12)]² = π(6)² = 36π The area is 36π, which can be rounded to 113.10. 


Term

Definition
The region of a circle bounded by an arc of the circle and two radii. It looks like a triangle with a one rounded side (the arc). 


Term
What is the Ratio of the Area of a Sector of a Circle? 

Definition
The ratio of the area of a sector to the area of the circle is equal to the ratio of the degree measure of the arc to 360ᵒ. S/A = ∠b/360 Where S is the area of the sector, A is the area of the circle, and ∠b is the measure of the arc. 


Term
How Do You Calculate the Area of a Sector of a Circle? 

Definition
S = A(∠b/360) Where S is the area of the sector, A is the area of the circle, and ∠b is the measure of the arc. 


Term
If the Radius of a Circle is 6 and the Measure of an Arc is 45ᵒ, What is the Area of the Sector? 

Definition
S = A(45/360) We know that A = π(6)² = 36π, so: a = 36π(45/360) = 36π(0.125) = 4.5π The area of the sector is 4.5π or approximately 14.14. 


Term

Definition
A line that intersects the circle at exactly one point. 


Term

Definition
The point where a tangent intersects a circle. 


Term
Fill in the Blank: If a Line is Tangent to a Circle, then a ______ Drawn to the Point of Tangency is Perpendicular to the Tangent Line. 

Definition


Term
Fill in the Blank: If a Line is Tangent to a Circle, then a Radius Drawn to the ______ is Perpendicular to the Tangent Line. 

Definition


Term
Fill in the Blank: If a Line is Tangent to a Circle, then a Radius Drawn to the Point of Tangency is ______ to the Tangent Line. 

Definition


Term
Fill in the Blank: When All of the Vertices of a Polygon Lie on a Circle, the Polygon is ______ that Circle. 

Definition


Term
What Does it Mean to Say a Polygon is Inscribed in a Circle? 

Definition
All of the vertices of the polygon lie on the circle. 


Term
Fill in the Blank: When All of the Vertices of a Polygon Lie on a Circle, the Circle is ______ that Polygon. 

Definition


Term
What Does it Mean to Say a Circle is Circumscribed About a Polygon? 

Definition
All of the vertices of the polygon lie on the circle. 


Term
What Do You Know About an Inscribed Triangle if One Side of that Triangle is the Diameter of the Circle? 

Definition
The triangle is a right triangle. 


Term
What Do You Know About the Sides of an Inscribed Right Triangle Inside a Circle? 

Definition
One of the sides of the triangle is the radius of the circle. 


Term
Fill in the Blank: When All of the Sides of a Polygon Lie Are Tangent to a Circle, the Polygon is ______ that Circle. 

Definition


Term
What Does it Mean to Say a Circle is Inscribed in a Polygon? 

Definition
All of the sides of the polygon are tangent to the circle. 


Term
Fill in the Blank: When All of the Sides of a Polygon Lie Are Tangent to a Circle, the Circle is ______ that Polygon. 

Definition


Term
What Does it Mean to Say a Polygon is Circumscribed About a Circle? 

Definition
All of the sides of the polygon are tangent to the circle. 


Term

Definition
Two or more circles with the same center. 


Term
Fill in the Blank: Two or More Circles with the Same Center are ______. 

Definition


Term
What are the Basic ThreeDimensional Figures? 

Definition
Rectangular solids, cubes, cylinders, spheres, pyramids, and cones. 


Term

Definition
A threedimensional figure with six rectangular surfaces called faces. 


Term
How Many Faces Does a Rectangular Solid Have? 

Definition


Term
In a Rectangular Solid, Which Faces are Perpendicular to Each Other? 

Definition


Term
Fill in the Blank: In a Rectangular Solid, Adjacent Faces are ______ to Each Other. 

Definition


Term
What is an Edge of a Rectangular Solid? 

Definition
A line segment that is the intersection of two of its faces. 


Term
Fill in the Blank: Each Line Segment that is the Intersection of Two Faces of a Rectangular Solid is Called an ______. 

Definition


Term
What is a Vertex of a Rectangular Solid? 

Definition
A point where the edges intersect. 


Term
Fill in the Blank: Each Point at Which the Edges of a Rectangular Solid Intersect is Called a ______. 

Definition


Term

Definition
A rectangular solid with six square faces. The length, width, and height are the same (l = w = h). 


Term
How Many Edges Does a Rectangular Solid Have? 

Definition


Term
How Many Vertices Does a Rectangular Solid Have? 

Definition


Term
What Are the Dimensions of a Rectangular Solid? 

Definition
Length (l), width (w), and height (h). 


Term
What is the Volume of a Rectangular Solid? 

Definition
The product of its three dimensions. 


Term
How Do You Calculate the Volume of a Rectangular Solid? 

Definition


Term
What is the Surface Area of a Rectangular Solid? 

Definition
The sum of the areas of the six faces. 


Term
How Do You Calculate the Surface Area of a Rectangular Solid? 

Definition


Term
If a Rectangular Solid has a Length of 10, a Width of 4, and a Height of 6, What is its Volume? 

Definition


Term
If a Rectangular Solid has a Length of 10, a Width of 4, and a Height of 6, What is its Surface Area? 

Definition
A = 2[(10)(4)+(10)(6)+(4)(6)] A = 2(40+60+24) A = 2(124) A = 248 


Term

Definition
Two circular bases joined by a surface made of all line segments that join points on the two circles and are parallel to the line segment that joins the centers of the circles. 


Term

Definition
The line segment joining the centers of the two circular bases of a cylinder. 


Term

Definition
A circular cylinder whose axis is perpendicular to its bases. 


Term
What is the Height of a Right Circular Cylinder? 

Definition
The length of the line segment that connects the centers of the two circles that are its bases. 


Term
How Do You Calculate the Volume of a Right Circular Cylinder? 

Definition
V = πr²h Where r is the radius of the bases and h is the height of the cylinder. 


Term
What is the Surface Area of a Circular Cylinder? 

Definition
The sum of the areas of the two bases and the lateral area. 


Term
How Do You Calculate the Surface Area of a Right Circular Cylinder? 

Definition
A = 2(πr²) + 2πrh Where r is the radius of the bases and h is the height of the cylinder. 


Term
If a Right Circular Triangle Has a Height of 8 and a Radius of 3, What is its Volume? 

Definition
V = π(3)²(8) V = π(9)(8) V = 72π Which is approximately 226.19. 


Term
If a Right Circular Triangle Has a Height of 8 and a Radius of 3, What is its Surface Area? 

Definition
A = 2[π(3)²] + 2π(3)(8) A = 2[π(9)] + 2π(24) A = π(18) + π(48) A = 18π + 48π A = 66π Which is approximately 207.35. 

