Proving Angles Congruent Geometry 2-5
Adjacent angles – Two coplanar angles that share a common side, a common vertex and no interior points Complementary Angles – Two angles whose measures have a sum of 90 Supplementary Angles – Two angles whose measures have a sum of 180 Angles
How to use a protractor Review
Investigation
Linear pair – two angles formed from a ray and a line 1 2 Definition
If two angles form a linear pair, then the measures of the angles add up to 180° 2 Conjecture
Prove this on a chromebook 1 2 Conjecture
Geogebra.org
Or, maybe… Geogebra.org
Geogebra.org
Add an algebra perspective, so we can do some math Geogebra.org
Turn off the axis, so geometry looks much cleaner Geogebra.org
Select the line segment tool Geogebra.org
Add two line segments as shown Geogebra.org
Select the angle measurement tool Geogebra.org
Geogebra.org Measure each angle by clicking on the points Click in a counterclockwise order Geogebra.org
Geogebra.org Use the move tool to click and move The angle measurements Geogebra.org
Type this formula in the list on the left Type this formula in the list on the left. To find the greek letters, use the pop-up keyboard on the bottom
Use the move tool to move line segments around, specifically point D Use the move tool to move line segments around, specifically point D. Watch what happens to the addition of the two angles.
Investigation
Investigation
Vertical Angles – opposite angles formed from intersecting lines 1 2 Definition
If two angles are vertical angles then they have equal measures 1 2 Conjecture
Complete this yourself on Geogebra 1 2 Conjecture
Proofs
Proofs can be in different forms
We have proven this, we never have to prove it again, and we can use this theorem to help other proofs. Angles
Find the measure of each lettered angle without using a protractor 112° 112° 68° 68° 112° Examples
Find the measure of each lettered angle without using a protractor 20° 70° 20° 110° 70° Examples
Find the measure of each lettered angle without using a protractor 90° 163° 110° 27° 70° Examples
Angles
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Angles - Practice
Pages 100 – 102 1-19, 21, 29, 31, 35, 41, 48, 50 Homework