- Jorge Cássio
- Angles, Straight Lines
Parallel Lines - Definition
Two lines are parallel if, and only if, they coincide (that is, equal) or are coplanar and have no common point.
Which pairs of lines are parallel? (use the "Show / Hide angle marks" box to help you)
Angles determined by parallel and transversal lines
In the previous structure, which pairs of angles are congruent?
In the previous structure, which of the following pairs of angles are supplementary?
Alternate Interior Angle Theorem (Alternate for the previous theorem)
Constructing a parallel line
In the following GeoGebra applet, follow the steps below: - Select the POINT (Window 2) and draw a point B on line r. - Select the COMPASS tool (Window 6). Then click on point A and point B (it will open the compass) and again on point A (it will close the compass and form a circle). After that click on point B and point A (it will open the compass) and again on B (it will close the compass and form a second circle). - Select the INTERSECT (Window 3) and mark the intersection C of the last circle with the line r. - Select the COMPASS (Window 6). Then click on point C and point A (it will open the compass) and again on point B (it will close the compass and form a circle). - Select the option INTERSECT (Window 3) and mark point D, which is the upper intersection of the first circunference with the third circunference. -Select the option LINE (Window 3) and click on point A and point D. Label this line s. - Select the option SHOW / HIDE OBJECT (Window 7) and hide the circles, points B, C and D, leaving only the lines and point A. -Select the option RELATION (Window 8) and click on the two lines. What happens? - Select the option MOVE (Window 1) move point A or line r. What can you see?
Write an argument to justify the construction.
Exterior Angles of a Triangle
Triangle Exterior Angle Theorem
Interior angles of the triangle (source: https://www.geogebra.org/luisclaudio)
Move the selector "t". Also move the vertices of the triangle. What can you see?
Explain the previous property.