Tests will be graded for the next block. If you have not taken the Similarity Test, you need to take it during A&E tomorrow.
Today was a big content day in Pre-AP Geometry.
There are two big ideas that mesh together:
Right triangles (similar) with angles of 30-60-90 degrees have a predictable ratio that can be used to find missing sides: if the short leg is x, the the hypotenuse is 2x, and the long leg is x times the square root of 3. So if you know one side, you can find the other two. Isosceles right triangles (all similar) have angles of 45-45-90 degrees. If the legs of a 45-45-90 are "a" in length, then the hypotenuse is "a times the square root of 2".
We also worked at the algebra required to simplify radicals so that we can keep our answers in exact form, and so we can work better with the "Pythagorean Shortcuts" mentioned above. (2 special ratios)
In most classes, we did the "geometric model" on dot paper. And in 2 classes, we proved the Pythagorean Theorem.
HW #7 is 1-14, and 17 on the attached document PLUS pp 507-8:1-12 and 17. On the handout, copy the problem and show work. On pp 507-8, do not use the Pythagorean Theorem. Try to find the missing sides with the shortcuts (unless the triangle is not one of the special angle measures).
Today was a big content day in Pre-AP Geometry.
There are two big ideas that mesh together:
Right triangles (similar) with angles of 30-60-90 degrees have a predictable ratio that can be used to find missing sides: if the short leg is x, the the hypotenuse is 2x, and the long leg is x times the square root of 3. So if you know one side, you can find the other two. Isosceles right triangles (all similar) have angles of 45-45-90 degrees. If the legs of a 45-45-90 are "a" in length, then the hypotenuse is "a times the square root of 2".
We also worked at the algebra required to simplify radicals so that we can keep our answers in exact form, and so we can work better with the "Pythagorean Shortcuts" mentioned above. (2 special ratios)
In most classes, we did the "geometric model" on dot paper. And in 2 classes, we proved the Pythagorean Theorem.
HW #7 is 1-14, and 17 on the attached document PLUS pp 507-8:1-12 and 17. On the handout, copy the problem and show work. On pp 507-8, do not use the Pythagorean Theorem. Try to find the missing sides with the shortcuts (unless the triangle is not one of the special angle measures).
jan_28-29_warm-up.pdf |
hw_handout_for_simplifying_radicals.pdf |
notes_and_practice_10.1-2.pdf |