Triangle sum theorem: the angles add up to 180°
Exterior angle is supplementary to the interior angle.
can have ONE 90° angle OR ONE obtuse angle.
180°/3 = 60° equiangular
3 variables (x,y,z)
Pair 2 equations, eliminate one letter.
Pair different 2 equations and eliminate the SAME letter.
Use the new equations with 2 letters to eliminate again.
Triangle sum postulate: the angles of a triangle add to 180°.
Exterior angles are supplementary.
43°+82°+x=180° triangle sum postulate
Triangle: 180/3 = 60° equiangular
Only ONE angle can be right OR obtuse.
Quest 32 was to have students practice inequalities. Here is the link to the activity: http://www.quia.com/quiz/3377503.html
Remember you must demonstrate mastery learning. Scoring less than 70% is not demonstrating that you’ve learned it. You need to persevere and keep trying!!
Here is a website with some quick information: http://regentsprep.org/REgents/math/ALGEBRA/AE85/GrIneqa.htm
If you can graph a straight line, you can graph an inequality!
Graphing an inequality starts by graphing the corresponding straight line. After graphing the line, there are only two additional steps to remember.
||Choose a point not on the line and see if it makes the inequality true. If the inequality is true, you will shade THAT side of the line — thus shading OVER the point. If it is false, you will shade the OTHER side of the line — not shading OVER the point.
||If the inequality is LESS THAN OR EQUAL TO or GREATER THAN OR EQUAL TO, the line is drawn as a solid line. If the inequality is simply LESS THAN or GREATER THAN, the line is drawn as a dashed line.
Graphing an Inequality
|1. Solve the equation for y (if necessary).
2. Graph the equation as if it contained an = sign.
3. Draw the line solid if the inequality is or
4. Draw the line dashed if the inequality is < or >
5. Pick a point not on the line to use as a test point.
The point (0,0) is a good test point if it is not on
6. If the point makes the inequality true, shade that
side of the line. If the point does not make the
inequality true, shade the opposite side of the line.
Graph the following inequality
y 3x – 1
Graph the inequality
y 3x – 1
1. Graph the line y = 3x – 1.
2. Pick a test point. (0,0) was used.
3. The test point is false in the inequality
0 3(0) – 1
0 -1 false
4. Since the test was false, do not shade OVER the point (0,0) — shade the opposite side of the line.
5. The line, itself, is SOLID because this problem is “less than or EQUAL TO.”
If a point is in the shaded region then it is a solution. If it is not in the shaded region it is NOT a solution.
Knowing where to shade…
1) Graph the line (< or > is a dotted line)
2) suggestion to express in y = mx + b form where y is alone in his home.
3) if y is alone in his home then less than (<) is under the line and greater than (>) is above the line.
BEWARE if y is not alone in his home!!!