Lesson 1.2.6: Unknown Angle Proofs (Proofs of known facts) |
For this lesson there are 10 steps for you to take. Scroll down and do each step one-by-one. The instructions under each step will help clarify exactly what you need to do, so please read all the instructions.
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Here is the Lesson 1.2.6 Worksheet
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1.) Start your notes
Watch this video and take notes. You should have the title, target, and vocab done after this video. |
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2.) Read and Prove
Once a theorem has been proved, it can be added to our list of known facts and used in proofs of other theorems. For example, in Lesson 1.2.4 we proved that vertical angles are of equal measure, and we know that if a transversal intersects two parallel lines, alternate interior angles are of equal measure. How do these facts help us prove that corresponding angles are congruent? Using the Vertical Angles Theorem, the Alternate Interior Angles Theorem, and the diagram to the right, prove that corresponding angles are congruent. |
3.) Video: Corresponding Angles Proof
Watch this video to see how I used our two previously known facts to prove that corresponding angles of parallel lines are congruent. |
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4.) Prove that... Same-Side Interior Angles
Use any or all of the 3 facts that we now have to prove that interior angles on the same side of the transversal are supplementary. Add any necessary labels to the diagram below, then write out a proof including given facts and a statement of what needs to be proved. |
5.) Video: Same-Side Interior Angles Proof
Watch this video to see how I used our previously known facts to prove that same-side interior angles of parallel lines are supplementary. |
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7.) Video: Triangle Sum Proof
Watch me prove that the interior angles of a triangle always add up to 180 degrees. |
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8.) Video: Eratosthenes Solves a Puzzle
Take a moment to take a look at one of those really famous Greek guys we hear so much about in geometry – Eratosthenes. Over 2,000 years ago, Eratosthenes used the geometry we have just been working with to find the diameter of Earth. He did not have cell towers, satellites, or any other advanced instruments available to scientists today. The only things Eratosthenes used were his eyes, his feet, and perhaps the ancient Greek equivalent to a protractor. Watch this video to see how he did it, and try to spot the geometry we have been using throughout this lesson |
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