180 - x = 3(90 - x)

Suppose that the diagram showed, in blue, all the points that are 5 cm from P. What geometric figure would the points form?

In a more complete diagram, would there be a red point 15 cm from both F and 7? How many such points?

It appears as if points P, X, and T might lie on a straight line. Use a ruler or the edge of a sheet of paper to see if they do.

It looks as if P might be equidistant from F and X. Is it?

Suppose Pat spoke of a line / joining F and T while you thought of a line n joining F and T. Is it better to say that./ and n are two different lines, or to say that we have one line with two different names?

Point X is equidistant from F and T. Furthermore, point Y is equidistant from F and T. Does that mean that X and Y are equally distant from F?

Suppose you were asked to find a point 5 cm from P. 5 cm from F, and 5 cm from T. Is there such a point?

Do you believe there is any point that is equidistant from P. F. and r?

In the diagram a, b, c, and d are lengths. Which is greater, the product ab or the product cdft

A path between opposite vertices of the square is made up of hundreds of horizontal and vertical segments. (The diagram shows a simplified version.) What is the best approximation to the length of the path24, 34, 44, or more than 44?

Name a fourth point that is in the same plane as the given points. A, B, C

Name a fourth point that is in the same plane as the given points. E. F. H

Name a fourth point that is in the same plane as the given points. D. C, H

Name a fourth point that is in the same plane as the given points. A. D, E

Name a fourth point that is in the same plane as the given points. B. E. F

Name a fourth point that is in the same plane as the given points. B. G. C

Are there any points in CG besides C and G?

Are there more than four points in plane ABCD?

Name the intersection of planes ABFE and BCGF

Name two planes that do not intersect.

Name two planes that intersect in FG.

Name three lines that intersect at point E.

Name three planes that intersect at point B.

a. Are points A, D, and C collinear? b. Are points A, D, and C coplanar?

a. Are points R, 5, G, and F coplanar? b. Are points R, S, G, and C coplanar?

a. Name two planes that do not intersect. b. Name two other planes that do not intersect.

Can two horizontal planes intersect?

a. Can two vertical planes intersect? b. Suppose a line is known to be in a vertical plane. Does the line have to be a vertical line?

Vertical line / intersects a horizontal plane M at point O. line / intersects a horizontal plane M at point O.

Horizontal plane P contains two lines k and n that intersect at point A.

Horizontal plane Q and vertical plane N intersect.

Vertical planes X and Y intersect in AB.

Point P is not in plane N. Three lines through point P intersect N in points A , B, and C.

Three vertical planes intersect in a line.

A vertical plane intersects two horizontal planes in iines / and n.

Three planes intersect in a point.

12 + 3b = 2 + 5b

4c + 23 = 9c - 7

7/j + (90 - h) = 210

5x + (180 - jc) = 300

(4/ + 5) + (5/ + 40) = 180

Og - 4) + (4g + 10) = 90

2(4d + 4) = d +1

2(d + 5) = 3(d - 2)

180 - x = 3(90 - x)

3(180 - y) = 2(90 - y)

On AB, how many points are there whose distance from point B is 3 cm?

The Ruler Postulate suggests that there are many ways to assign coordinates to a line. The Fahrenheit and Celsius temperature scales on a thermometer indicate two such ways of assigning coordinates. A Fahrenheit temperature of 32 corresponds to a Celsius temperature of 0. The formula, or rule, for converting a Fahrenheit temperature F into a Celsius temperature C is C = -(F 32). a. c. What Celsius temperatures correspond to Fahrenheit temperatures of 212 and 98.6? Solve the equation above for F to obtain a rule for converting Celsius temperamrcs to Fahrenheit temperatures. What Fahrenheit temperatures correspond to Celsius temperatures of - 40 and 2000?