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

Demo? 1 2 Conjecture

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

Demo? 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

Homework Pages 100 – 102 Day one: 1-19 Day two : 21, 29, 31, 35, 41, 48, 50 Homework

Honors Homework Pages 100 – 102 Day one: 1-19 Day two : 21, 29, 31, 35, 41, 48, 50, 55 Honors Homework