Proving Angles Congruent

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2-5 Proving Angles Congruent

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Presentation transcript:

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