Math TEST December 4, 2018

Dear 8th grade Math parents,

We will have our next test on Tuesday. Your child has a green review packet with practice questions to complete this weekend. They have notes in their notebook, but I will list the basics below . . .

1) The interior (inside) angles in a triangle add up to 180. The exterior (outside) angles add up to 360.

Now instead of 100 + 40 + ___ = 180 there will be expressions given for each angle and they have to create an equation like:

3x +5 + 4x +25 + x +30 = 180 After solving, they plug in x to find the angles.

2) An exterior angle of a triangle equals the sum of the two remote interior angles. In other words, an angle outside the triangle is as big as the two inside angles (that are far away from it) put together. This will also involve creating an equation to solve and then plugging in the value of x.

3) Some students have trouble finding angles that are identified with 3 letters. Angle ACB will be found at the middle letter C. But it may be one of several angles centered there. So they have to mentally trace a path that goes from point A to C to B to identify the correct one.

4) TRANSVERSALS: Two parallel lines crossed by another line create two sets of 4 angles. The students know that:

A) Opposite angles are equal,

B) that corresponding angles are equal (e.g. upper left = upper left . . . )

C) that supplementary angles (pairs of angles that form a straight line) add up to 180

D) If you give them just one angle in a transversal arrangement, they can find all the others

Again, this will involve setting up equations and solving them.

5) DILATIONS involve MULTIPLYING the x and y coordinates of points by a scale factor (a multiplier). If the scale factor were 2 for example, the motion rule would be (x,y) -> (2x, 2y) When you do this to every point in a figure, the process either expands the pre-image (if the multiplier is greater than one) or shrinks it (if the multiplier is a fraction between 0 and 1)

Some questions might involve giving you a pre-image and image on a graph, and having you figure out the scale factor. That is easily done by picking any pair of corresponding points and taking the new x divided by the old x.

The lengths of sides of a polygon that is dilated have the same ratio as the scale factor. If the scale factor is 3.5, then the sides on the image will be 3.5 times longer than those on the pre-image.

By the way, an apostrophe is used on vertices on the image (new figure) to show that they are the new points. So vertex A on the pre-image will show up as A' on the (new) image.

6) CONGRUENCE Same shape, same size. Congruence is basically a geometry was of saying "equal". Students must know that "Dilations do not preserve congruence." (If you dilate a figure, making it bigger or smaller, it will no longer match the original, although it will be SIMILAR.

7) ORIENTATION Figures share the same orientation if their vertices (corners) share the same relative positions to each other (e.g. if you go around a figure clockwise you should visit the same letters in the same order. Dilations may make the letters farther apart or closer together, but they do not change the relative positions. So we say that "Dilations preserve orientation."

This test is a little harder than most, so the students will need practice to be successful. Thanks for helping them!

Best regards,

Charles Wells

8th grade Math / Algebra

Aragon Middle School