Visual Glossary Unit 2A
The following section will encompass a neatly organized 'glossary' for the terms we have learned this unit through pictures, definitions, and examples.
This is an example of skew lines.
Skew Lines~ These are a pair of lines that are not coplanar. Skew lines are not parallel and do not intersect. There is no symbol for skew lines. Lines a and b are not on the same plane. Therefore, they are not parallel and will not intersect making them skew. This was included as it was new vocabulary that will come up later in math. |
This is an example of a transversal.
Transversal~It is a line that intersects two coplanar lines at two different points. Introduces new angle relations,etc.
Symbol~ No symbol for a transversal.
For example, line p intersecting the parallel lines a and b creates a transversal.
This was included because it is primary in finding angle relations and without this you an'y find angle measures in polygons or with lines.
Transversal~It is a line that intersects two coplanar lines at two different points. Introduces new angle relations,etc.
Symbol~ No symbol for a transversal.
For example, line p intersecting the parallel lines a and b creates a transversal.
This was included because it is primary in finding angle relations and without this you an'y find angle measures in polygons or with lines.
This is an example of a two-column proof.
Two-Column Proof~ This is a type of proof where the statements and corresponding reasons are listed in two columns with the statements in the left column and the reasons in the right column.
There is no symbol for a two-column proof.
In 2 column proofs, it helps you prove a statement. If the given statement was that it was cold outside and it was asking you to prove that it was freezing, you can see that the first statement is that it is cold. The second statement could be that the temperature is 28 degrees Fahrenheit. As a result, the reason could be that that is the temperature. Finally, the last statement is that it is freezing with a reason that it is below 32 degrees. This proved the statement that it is freezing.
This was included because proofs are the base of geometry. Without knowing ho to do a two-column proof, you'd be lacking the understanding of one type of proof work.
Two-Column Proof~ This is a type of proof where the statements and corresponding reasons are listed in two columns with the statements in the left column and the reasons in the right column.
There is no symbol for a two-column proof.
In 2 column proofs, it helps you prove a statement. If the given statement was that it was cold outside and it was asking you to prove that it was freezing, you can see that the first statement is that it is cold. The second statement could be that the temperature is 28 degrees Fahrenheit. As a result, the reason could be that that is the temperature. Finally, the last statement is that it is freezing with a reason that it is below 32 degrees. This proved the statement that it is freezing.
This was included because proofs are the base of geometry. Without knowing ho to do a two-column proof, you'd be lacking the understanding of one type of proof work.
This is an example of corresponding angles.
Corresponding Angles~ 2 angles that lie on the same side of the transversal and on the same side of the other two lines. One angle is interior and one is exterior. Given that the two lines are parallel, they are equal/congruent.
There is no symbol for corresponding angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. Since there are two angles that are on the same side of the transversal, they are on the same side of the other two lines, and one angle is interior and the other is exterior, then the lines are therefore corresponding which subsequently causes the two angles to be congruent.
This was included as it is one of the many foundation angle relations in geometry.
Corresponding Angles~ 2 angles that lie on the same side of the transversal and on the same side of the other two lines. One angle is interior and one is exterior. Given that the two lines are parallel, they are equal/congruent.
There is no symbol for corresponding angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. Since there are two angles that are on the same side of the transversal, they are on the same side of the other two lines, and one angle is interior and the other is exterior, then the lines are therefore corresponding which subsequently causes the two angles to be congruent.
This was included as it is one of the many foundation angle relations in geometry.
This is an example of alternate interior angles.
Alternate Interior Angles~ These are 2 angles that are nonadjacent angles that lie on opposite sides of the transversal and between the other two lines. They are both interior and given that the two lines are parallel, they are congruent.
There is no symbol for alternate interior angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. The two angles are both on opposite sides of the transversal and are between the other two lines. Therefore these two angles are alternate interioro angles and are also congruent.
This was included as it is one of the many foundation angle relations in geometry.
Alternate Interior Angles~ These are 2 angles that are nonadjacent angles that lie on opposite sides of the transversal and between the other two lines. They are both interior and given that the two lines are parallel, they are congruent.
There is no symbol for alternate interior angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. The two angles are both on opposite sides of the transversal and are between the other two lines. Therefore these two angles are alternate interioro angles and are also congruent.
This was included as it is one of the many foundation angle relations in geometry.
This is an example of Alternate Exterior Angles.
Alternate Exterior Angles~ 2 angles that lie on opposite sides of the transversal and outside the other two lines.Given that the two lines are parallel, these two angles are also congruent.
There is no symbol for alternate exterior angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. In addition, the two lines are on oposite sides of the transversal and outside both of the two lines. The two angles are congruent and they are therefore alternate exterior angles.
This was included as it is one of the many foundation angle relations in geometry.
Alternate Exterior Angles~ 2 angles that lie on opposite sides of the transversal and outside the other two lines.Given that the two lines are parallel, these two angles are also congruent.
There is no symbol for alternate exterior angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. In addition, the two lines are on oposite sides of the transversal and outside both of the two lines. The two angles are congruent and they are therefore alternate exterior angles.
This was included as it is one of the many foundation angle relations in geometry.
This is an example of same side interior angles.
Same Side Interior Angles~ lie on the same side of the transversal and between the other two lines. Given that the two lines are parallel, they are supplementary.
There is no symbol for same side interior angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. Since the two angles are on the same side of the transversal and are between the two other lines. The angles are also supplementary because line a and b are parallel which means they are same side interior angles.
This was included as it is one of the many foundation angle relations in geometry.
Same Side Interior Angles~ lie on the same side of the transversal and between the other two lines. Given that the two lines are parallel, they are supplementary.
There is no symbol for same side interior angles.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. Since the two angles are on the same side of the transversal and are between the two other lines. The angles are also supplementary because line a and b are parallel which means they are same side interior angles.
This was included as it is one of the many foundation angle relations in geometry.
This is an example of the Converse of Corresponding Angles Theorem
Converse of Corresponding Angles Theorem~ If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.
There is no symbol for the converse of the corresponding angles theorem.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. You can see that two angles are equal. Since one angle so interior and one is exterior, there's two angles are corresponding angles. In order to prove that lines a and b are parallel, you use the converse of corresponding angles theorem. Since they are corresponding angles,the two lines line a and line b are parallel.
This was included as it is an example of the way lines are proved as parallel using angle relationships and measures.
Converse of Corresponding Angles Theorem~ If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.
There is no symbol for the converse of the corresponding angles theorem.
In this diagram, line l intersects two lines- line a and line b. Therefore, this creates a transversal. You can see that two angles are equal. Since one angle so interior and one is exterior, there's two angles are corresponding angles. In order to prove that lines a and b are parallel, you use the converse of corresponding angles theorem. Since they are corresponding angles,the two lines line a and line b are parallel.
This was included as it is an example of the way lines are proved as parallel using angle relationships and measures.
This is an example of a great circle.
Great Circle~ the equivalent of a line in spherical geometry.
There is no symbol for the converse of a great circle.
In this diagram, circle A is shown. There is a great circle shown around it. this is a line in spherical geometry that stretches all the way around the entire sphere.
This is included because it is one of the foundation aspects of spherical geometry.
Great Circle~ the equivalent of a line in spherical geometry.
There is no symbol for the converse of a great circle.
In this diagram, circle A is shown. There is a great circle shown around it. this is a line in spherical geometry that stretches all the way around the entire sphere.
This is included because it is one of the foundation aspects of spherical geometry.
Visual Glossary Unit 2B
This is an example of a reflection.
Reflection~ A reflection is a transformation across the line of reflection
in which each point in the preimage is the same distance from
the line of reflection as the corresponding point in the image.
There is no symbol for a reflection.
Rectangle ABCD is reflected across the line y=4 to create A'B'C'D'. This is an isometry.
This was included because it is one of the major transformations in geometry.
Reflection~ A reflection is a transformation across the line of reflection
in which each point in the preimage is the same distance from
the line of reflection as the corresponding point in the image.
There is no symbol for a reflection.
Rectangle ABCD is reflected across the line y=4 to create A'B'C'D'. This is an isometry.
This was included because it is one of the major transformations in geometry.
This is an example of an isometry.
Isometry~ This is a transformation that does not change the shape or size of a figure.
There is no symbol for an isometry.
Figure A was translated to become Figure B and the figure didn't change size or shape.
This was included because it is an important vocab term. It is solely the only term used for transformation of this sort and transformations in this category are referred to as these and you must be able to recognize the term.
Isometry~ This is a transformation that does not change the shape or size of a figure.
There is no symbol for an isometry.
Figure A was translated to become Figure B and the figure didn't change size or shape.
This was included because it is an important vocab term. It is solely the only term used for transformation of this sort and transformations in this category are referred to as these and you must be able to recognize the term.
This is an example of a line of reflection.
Line of Reflection~ The line over which an object/figure is reflected over to create another figure.
There is no symbol for a line of reflection.
The rectangle pre-image was reflected over the line of reflection to create the image.
This was included because it is one of the major transformations in geometry.
Line of Reflection~ The line over which an object/figure is reflected over to create another figure.
There is no symbol for a line of reflection.
The rectangle pre-image was reflected over the line of reflection to create the image.
This was included because it is one of the major transformations in geometry.
This is an example of a translation.
Translation~ A translation is a transformation along a vector such that each segment joining a point and its image has the same length as the vector and is parallel to the vector.
There is no symbol for a translation.
Figure ABCD is translated with a vector of a positive "X" value and a negative "Y" value causing the translation to result in A' B' C' D' to be in the fourth quadrant.
This was included because it is one of the major transformations in geometry.
Translation~ A translation is a transformation along a vector such that each segment joining a point and its image has the same length as the vector and is parallel to the vector.
There is no symbol for a translation.
Figure ABCD is translated with a vector of a positive "X" value and a negative "Y" value causing the translation to result in A' B' C' D' to be in the fourth quadrant.
This was included because it is one of the major transformations in geometry.
This is an example of a composition of transformations.
Composition of Transformations~ This is one transformation followed by another. Multiple combinations result in different outcomes.
There is no symbol for a composition of transformations.
Figure A was reflected over the line X= -2. That image was reflected over the line X= 2. As a result the composition of the two parallel lines that the image was reflected over resulted in a reflection.
This was included because it is important to know what happens when multiple transformations are utilized on a figure in a series that causes the figure to change differently.
Composition of Transformations~ This is one transformation followed by another. Multiple combinations result in different outcomes.
There is no symbol for a composition of transformations.
Figure A was reflected over the line X= -2. That image was reflected over the line X= 2. As a result the composition of the two parallel lines that the image was reflected over resulted in a reflection.
This was included because it is important to know what happens when multiple transformations are utilized on a figure in a series that causes the figure to change differently.
This is an example of a dilation.
Dilation~ It is a transformation in which the lines connecting every point P with its image P' all intersect at a point C, called the center of dilation, and is the same for every point P.
There is no symbol for a dilation.
Triangle ABC is dilated as a reduction because the image is smaller than the pre image. A reduction is an example of a dilation.
This was included because it is one of the major transformations in geometry.
Dilation~ It is a transformation in which the lines connecting every point P with its image P' all intersect at a point C, called the center of dilation, and is the same for every point P.
There is no symbol for a dilation.
Triangle ABC is dilated as a reduction because the image is smaller than the pre image. A reduction is an example of a dilation.
This was included because it is one of the major transformations in geometry.
This is an example of a rotation.
Rotation~ A rotation is a transformation about a point P, called the
center of rotation, such that each point and its image are the
same distance from P, and such that all angles with vertex P
formed by a point and its image are congruent.
There is no symbol for a rotation.
Figure A is rotated 90 degrees counterclockwise around the origin which would make the origin point P.
This was included because it is one of the major transformations in geometry.
Rotation~ A rotation is a transformation about a point P, called the
center of rotation, such that each point and its image are the
same distance from P, and such that all angles with vertex P
formed by a point and its image are congruent.
There is no symbol for a rotation.
Figure A is rotated 90 degrees counterclockwise around the origin which would make the origin point P.
This was included because it is one of the major transformations in geometry.
This is an example of an enlargement.
Enlargement~ A dilation that causes the image to be greater in area than the pre-image.
There is no symbol for an enlargement.
A'B'C'D' is an enlargement of ABCD and is greater in size/area.
This was included because it was an example of one of the two ways dilations are used in the growing and reduction of shapes/figures.
Enlargement~ A dilation that causes the image to be greater in area than the pre-image.
There is no symbol for an enlargement.
A'B'C'D' is an enlargement of ABCD and is greater in size/area.
This was included because it was an example of one of the two ways dilations are used in the growing and reduction of shapes/figures.
~Aniket Matharasi