Construction
What does bisector mean?
A bisector is a line that divides a line or an angle into two equivalent parts.
Find the point M, that divides segment AB into a ratio of 2:3 if A is (0,10) and B is (5,0)
(0,6) + (2,0)
=(2,6)
A(0,1)
B(3,1)
C(3,5)
Rectangle ABCD has the coordinates shown:
What are the coordinates of D?
D(0,5)
What are supplementary angles?
What are complementary angles?
Supplementary: Two angles that add up to 180
Complementary: Two angles that add up to 90
What is the distance between (0,1) (2,3)?
d=square root of 8
-First, use a straightedge to draw a line. Mark a point on the line.
-Second, place the compass point at A, and open the compass to measure length AB.
-Last, use the same setting/length and place the compass on the point and draw an arc through the line.
Find the point M that is two-thirds of the distance from A(-3, 6) to B(6,12)
2/3(6,12)+1/3(-3,6) ***B is closer the point M***
(4,8)+(-1,2)
=(3,10)
Could the points (0,0),(0,3), (4,0) form a right triangle? Explain
Yes, a2+b2=c2
32+42=52
Looking at the figure (Angles) on Schoology, Which angles are congruent to angle DEF?
ABC, any angle that is corresponding, or alternate exterior
Points A, B, and C are collinear. Point B is between A and C. Find the value of x.
AC = 17
AB = 5x + 2
BC = 3x - 1
5x+2+3x-1=17
x=2
What is the second step in making a copy of angle ABC?
Place the compasses on point B, set to any convenient width. Draw an arc across both sides of the angle, creating the points J and K as shown.
Consider the line segment PQ with endpoints P(-1,4) and Q(6,2). which point divides the line segment directed from P to Q in the ratio of 2:3?
3/5(-1,4)+2/5(6,2) *** P is closer to the point***
(-3/5,12/5)+(12/5,4/5)
=(9/5,16/5)
If the center of a circle is (2,1), and it has a radius of 6, which is another point on the circle?
A. (-4,1)
B. (0,5)
C. (-3,3)
D. (2.5, 3.5)
A. (-4,1)
distance between (2,1) and (-4,1) is 6 (using distance formula)
Looking at the figure (Angles) on Schoology,if angle DEB is 70 degrees, find the measure of angle CBE and angle ABC
CBE = 70 (alternate interior)
ABC = 110
Points A, B, and C are collinear. Point B is between A and C. Find the value of x.
AC = -3x - 9
AB = -5x + 2
BC = 29
-5x+2+29=-3x-9
-5x+31=-3x-9
40=2x
x=2
Place the steps in the correct order to construct a copy of the angle?
A. Without changing the compass's width, place the compass's point on P and draw a similar arc there, creating point M where the arc crosses PQ. Set the compass on K and adjust its width to point J
B. Make a point P that will be the vertex of the new angle. From P, draw a ray PQ. This will become one side of the new angle.
C. Without changing the compass's width, move the compass to M and draw an arc across the first one, creating point L where the two arcs cross. Draw a ray PR from P through L and onwards a little further.
D. Place the compass on point B, set to any convenient width. Draw an arc across both sides of the angle, creating the points J and K.
D->B->C->A
Consider the line segment PQ with endpoints P(-2,-4) and Q(3,-2). which point divides the line segment directed from P to Q in the ratio of 2:5?
5/7(-2,-4)+2/7(3,-2)
(-10/7,-20/7)+(6/7,-4/7)
=(-4/7,-24/7)
Could the points (0,1),(2,3), (4,5) form a right triangle? Explain
No, Pythagorean Theorem does not work here.
Using distance formula, we can get all 3 side lengths of the triangle
a2+b2 does NOT equal c2 in this case
Write the converse of the conditional statement and determine its truth value:
If an angles has a measure of 70 degrees, then it is an acute angle
If an angle is acute, then is has a measure of 70 degrees.
False, it could be any angle less than 90, not just 70
If the center of a circle is (-1,2), and one of the endpoints is at (-1,-4), what is the radius?
radius = 6
Draw a perpendicular bisector and midpoint.
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________|________
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Find the point M that is two-sevenths of the distance from A(-2, 5) to B(4,10)
5/7(-2,5)+2/7(4,10)
(-10/7,25/7)+(8/7,20/7)
=(-2/7,45/7)
A(-2,1)
B(5,1)
C(5,5)
Rectangle ABCD has the coordinates shown:
What are the coordinates of D?
Looking at the figure (Angles) on Schoology,if angle CBE is 45 degrees, find the measure of angle DEF and angle ABC
DEF = 135
ABC = 45 (alternate exterior)
What does collinear mean?
Collinear points are a set of three or more points that exist on the same straight line