GEOMETRY – TOWARDS A PARTY That one theorem you’ve wanted to say but just haven’t been able to.

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Presentation transcript:

GEOMETRY – TOWARDS A PARTY That one theorem you’ve wanted to say but just haven’t been able to

INITIAL TASK(S) 1.Converse with your team and write your explanation for #12 on the board under your group number 2.Log onto socrative (436395) – answer the review questions (you may look back over your notes) (this will constitute a grade! If you are having technical difficulties with socrative, raise your hand).  NOTE: The last question on socrative asks you to judge the explanations written on the board. If you get there and less than ½ of the explanations are up, hang tight on socrative and move to the next task. 3.Complete the rest of your classwork 4.1 and post it to your google drive. 4.Done before the rest??  Help your group mates  If the whole group finishes all tasks, raise your hand (not until each person in the group has submitted classwork 4.1)

SO…WHAT DO WE MAKE OF THIS??

LETS BREAK IT DOWN What are we trying to prove?? Given: Prove:

KEEP IT GOING… Given: Prove: Indirect assumption??

AND WE’RE BACK HERE Given: Prove: Indirect AssumptionGiven Definition of congruence We can draw a line through point B to create Soooo….can we reach a contradiction?

EUCLIDS 5 TH POSTULATE If point P is not on a line “l” there exists one and only one line through point P that is parallel to line “l”.

BACK HERE AGAIN Given: Prove: Indirect AssumptionGiven Definition of congruence We can draw a line through point B to create Soooo….can we reach a contradiction?

REVIEW OF SOME IMPORTANT PROOFS Back to the beginning. Given If, then. Prove In the space provided, explain how we proved the theorem above. Hint: Use the diagram below to help you with this indirect reasoning!

MAKE SURE YOU’VE GOT THIS!

4.1 THEOREMS

PRACTICE! SOMETIMES, ALWAYS, NEVER Alternate interior angles are ______ supplementary. IF and, then point E is _____________ on If the exterior angle is acute, then the remote interior angles are ____________ acute.

PRACTICE: USING PARALLEL LINES TO SOLVE Which lines, (if any) on the right are parallel? Justify your reasoning.

USING EXTERIOR ANGLE Fill in the following with M<3 ______ m<6 M<7 ______ m<6 JI ________ IH M<EHG __________ m<9 m<2 __________ m<6 m<2 __________ m<7 M<8+m<2 _____ 180