2a - 7 3a + 10

2a – 7 = 3a + 10

Vertical <‘s are ≅

(3,8)

(4,-1)

How do you find the center of this circle?

218,

243 The center of a

circle is the midpoint of any

diameter.

2x + 8 6 x - 84

Definition of Linear pair– 2 angles that are adjacent and supplementary

2x + 8 + 6x – 84 = 180

2x + 184x

Definition of perp. lines - 2 lines that intersect to form a right angle

Definition of complementary <‘s - 2 angles whose sum = 90 degrees

AB is on a number line. Explain how to find its midpoint.

A + B 2A _____ has no size, no

dimensions, just position.

Point

Write the standard equation of a circle.

(x – h )² + (y – k )² = r²

Simplify √175

5√7

3x + 20

8x - 5

Solve for x. Explain your answer.

3x + 20 = 8x – 5

vertical angles are congruent

__________ is the set of all points.

Space

4 _____ points determine space.

noncoplanar

The midpoint of GD is (4,-5) and the coordinates of D are (-3,1). Find the coordinates of G.

___________________________________G M D(4, -5) (-3,1)

Double the midpoint and do the opposite of the given endpoint.

Step 1 --(8,-10)

Step 2---(+3,-1)

Answer (11,-11)

• What is the easiest way to prove a quad is a parallelogram?

• If the midpoints of the diagonals are the same.

What postulate is demonstrated here?

The intersection of 2 planes is a line.

• (2,5);(7,5);(-4,5)

• Points on the same line because all the y-coordinates are the same.

• y = 5

• Horizontal line

(3,2), ( 3, -1), (3, 7)

Points on the same line because all the x’s are the same

Vertical line

X=3

• What is a conjecture?

• A conclusion you reach using inductive reasoning.

1.Write the Circle Equation

X ² + y² = 4

Center (0,0)

Radius = 2

A B

CD

E F

GH

Are the following points collinear, coplanar, or noncoplanar? (Why?)

H, G, C

Coplanar

Any 3 pts lie in a plane

F,B,E,A

Coplanar – ll lines

A B

CD

E F

GH D,C,E,H

Noncoplanar

Skew lines

Are the following points collinear, coplanar,

or noncoplanar? (Why?)

Points that are in space are ___________points.

Noncoplanar

•If a circle has a center (4,-5) and it is tangent to the y- axis, what would its equation look like?

(X-4)² + (y+5)²= 16

Radius = 4 (distance from y-axis)

•Write the equation of a circle for a circle with an area = 121 π and a center ( -10, 4).

(X+10)² + (y-4)² = 121

121π = πr²

121 = r²

M R P-26 -2

If R is the midpt of MP findMR=_____ RP=_____and the coordinate of R.

MP = -2 - -26 =24

MR = RP = 12 Def of midpt.

Coordinate of R = -2 – 12 = 14 or -26 + 12 = -14

(-2,7) (-2,-3)

Find the center of the above circle-which is the midpt. of the diameter.

(-2,2)

Find the radius of the above circle.r = 5

H E Y2X 5X-14 21

Write an equation.

7X = 35

X = 5

Name the postulate you used to write the above equation.

Segment Addition Postulate

Find the coordinate of E.

21- 25 = -4

• Find the midpoint of AB if you are on a number line .

• A+B• 2• If you are • in a plane.

x₁ + x₂ , y₁ + y₂ 2 2( )