January 6, 2014
DEMO APPLETS: These are Geogebra Labs that I have created to help you explore and learn Geometry concepts. Please use the scroll bar at the bottom of each applet to move the screen left or right. I have not learned how to size these properly to fit without scrolling yet, but I think you can manage.
NOTE: Previous APPLETS will be removed to improve load time on Weebly.
You may access GGB labs which are available when applets are removed.
DEMO APPLETS: These are Geogebra Labs that I have created to help you explore and learn Geometry concepts. Please use the scroll bar at the bottom of each applet to move the screen left or right. I have not learned how to size these properly to fit without scrolling yet, but I think you can manage.
NOTE: Previous APPLETS will be removed to improve load time on Weebly.
You may access GGB labs which are available when applets are removed.
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EMBEDDED APPLETS from here down have been removed.
A MIDLINE in a triangle is the segment connecting two midpoints of two of the sides of the triangle. There are three MIDLINES in every triangle. With all three midlines drawn, what can you say about the four smaller triangles that make up the original triangle? What evidence justifies these conclusions?
A MIDLINE or MIDSEGMENT in a trapezoid is the segment connecting the midpoints of the non-parallel sides.
Extended Parallel Proportions (picture below)
Proportions & Similar Triangles (picture below)
Central, Interior & Exterior Angle of Regular Polygons (picture)
Given a REGULAR POLYGON with n-congruent sides (...and n-congruent angles),
What is the measure of each of the following:
1) the central angle 2) ALL exterior angles 3) ONE exterior angle 4) ALL interior angles 5) ONE interior angle
What are the general formulas for the measures of each of these angles if you know the value of n?
Given a REGULAR POLYGON with n-congruent sides (...and n-congruent angles),
What is the measure of each of the following:
1) the central angle 2) ALL exterior angles 3) ONE exterior angle 4) ALL interior angles 5) ONE interior angle
What are the general formulas for the measures of each of these angles if you know the value of n?
Angle Bisector (picture)
What is the relationship between an angle and the two angles formed by an angle bisector?
What is the relationship between any point on the angle bisector and the two sides of the angle?
What is the relationship between an angle and the two angles formed by an angle bisector?
What is the relationship between any point on the angle bisector and the two sides of the angle?
What is a MEDIAN in a Triangle? (picture)
Be able to define what a median is and its properties after exploring this dynamic applet.
Be able to define what a median is and its properties after exploring this dynamic applet.
Three Medians in a Triangle (picture)
What is true about the point of concurrency of the medians of a triangle?
How does this point divide the median lengths?
Can you describe the purpose of the centroid after exploring the relationship using the 3rd checkbox?
What is true about the point of concurrency of the medians of a triangle?
How does this point divide the median lengths?
Can you describe the purpose of the centroid after exploring the relationship using the 3rd checkbox?
What is a PERPENDICULAR BISECTOR of a Triangle? (picture)
Be able to define an perpendicular bisector and its properties after exploring this dynamic applet.
RECALL: Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the bisected segment.
Be able to define an perpendicular bisector and its properties after exploring this dynamic applet.
RECALL: Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the bisected segment.
Three Perpendicular Bisectors of a Triangle (picture)
What is true about the point of concurrency of the three perpendicular bisectors of a triangle?
HINT: What is true about any point on the perpendicular bisector of a segment?
What is true about the point of concurrency of the three perpendicular bisectors of a triangle?
HINT: What is true about any point on the perpendicular bisector of a segment?
What is an ALTITUDE of a Triangle? (picture)
Be able to define an altitude and its properties after exploring this dynamic applet.
Be able to define an altitude and its properties after exploring this dynamic applet.
Three Altitudes of a Triangle APPLET
Where is the point of concurrency of the three altitudes in a triangle when the triangle is
acute, right and obtuse?
Using the last checkbox instructions, explain why A is the orthocenter of triangle BGC.
Explain why B is the orthocenter of triangle AGC.
Explain why C is the orthocenter of triangle AGB.
Where is the point of concurrency of the three altitudes in a triangle when the triangle is
acute, right and obtuse?
Using the last checkbox instructions, explain why A is the orthocenter of triangle BGC.
Explain why B is the orthocenter of triangle AGC.
Explain why C is the orthocenter of triangle AGB.
What is an ANGLE BISECTOR of a Triangle? (picture)
Be able to define an angle bisector and its properties after exploring this dynamic applet.
Be able to define an angle bisector and its properties after exploring this dynamic applet.
Three Angle Bisectors of a Triangle (picture)
What is true about the point of concurrency of the three angle bisectors of a triangle?
HINT: What is true about any point that lies on the angle bisector?
What is true about the point of concurrency of the three angle bisectors of a triangle?
HINT: What is true about any point that lies on the angle bisector?
ANGLE DEFINITIONS APPLET
ANGLE DEFINITIONS: Explore and be able to define four types of angles
COMPLEMENTARY, SUPPLEMENTARY, LINEAR PAIRS & STRAIGHT ANGLES.
ANGLE DEFINITIONS: Explore and be able to define four types of angles
COMPLEMENTARY, SUPPLEMENTARY, LINEAR PAIRS & STRAIGHT ANGLES.
TRIANGLE SUM APPLET
TRIANGLE SUM PROPERTY: The sum of the measures of a triangle is 180 degrees.
Can you explain why? Using logical deductive reasoning and what you know about
isometric transformations explain your reasoning?
TRIANGLE SUM PROPERTY: The sum of the measures of a triangle is 180 degrees.
Can you explain why? Using logical deductive reasoning and what you know about
isometric transformations explain your reasoning?
EXTERIOR ANGLES of a TRIANGLE APPLET
EXTERIOR ANGLES of a triangle and their related REMOTE INTERIOR ANGLES. What is the relationship between them?
EXTERIOR ANGLES of a triangle and their related REMOTE INTERIOR ANGLES. What is the relationship between them?
VERTICAL ANGLES APPLET
Use the next applet to learn what vertical angles are and what the relationship is between vertical angle pairs.
Use the next applet to learn what vertical angles are and what the relationship is between vertical angle pairs.
Vocab given TWO LINES cut by a TRANSVERSAL APPLET
Learn vocabulary and identify pairs of angles using the following applet.
Learn vocabulary and identify pairs of angles using the following applet.
3 APPLETS for five types of ANGLES
resulting from PARALLEL LINES cut by a TRANSVERSAL
The next THREE applets are for exploring the relationships between angle pairs for
1) CORRESPONDING ANGLES
2) ALTERNATE INTERIOR & ALTERNATE EXTERIOR ANGLES
3) SAME-SIDE INTERIOR & SAME-SIDE EXTERIOR ANGLES
When you are finished exploring these applets you should be able to
a) identify any of these angles
b) know the relationship between the angle pairs.
resulting from PARALLEL LINES cut by a TRANSVERSAL
The next THREE applets are for exploring the relationships between angle pairs for
1) CORRESPONDING ANGLES
2) ALTERNATE INTERIOR & ALTERNATE EXTERIOR ANGLES
3) SAME-SIDE INTERIOR & SAME-SIDE EXTERIOR ANGLES
When you are finished exploring these applets you should be able to
a) identify any of these angles
b) know the relationship between the angle pairs.