Page 189 - Math Course 2 (Book 2)

Postulates and Paragraph Proofs

Use Postulates Determine Valid Conclusions

Example Determine whether each statement is always,
sometimes, or never true. Explain.

Plane A and plane B intersect in exactly one point.
Determine whether the following statement is
always, sometimes, or never true. Explain. A .always
↔ ↔ B. sometimes
If plane T contains EF and EF contains point G, C. never
then plane T contains point G.
Answer
Always; Postulate 12.5 states
that if two points lie in a plane,
Answer
then the entire line containing
those points lies in the plane. Point N lies in plane X and point R lies in plane
Z. You can draw only one line that contains both
If two points lie in a line, then the entire line
12.5 containing those points lies in that plane. points N and R.

A .always
Determine whether the following statement is B. sometimes
always, sometimes, or never true. Explain C. never
↔
For XY, if X lies in plane Q and Y lies in plane R,
Answer
then plane Q intersects plane R.

Sometimes; planes Q and R can
be parallel (which means they
Answer Two planes will always intersect to form a line.
don’t intersect), and XY can
intersect both planes. A .always
B. sometimes
Determine whether the following statement is C. never

always, sometimes, or never true. Explain Answer
↔
GH contains three noncollinear points.

Never; noncollinear points do not
Answer
lie on the same line by definition.

Your Turn!

Determine Valid Conclusions

ART
Jodi is making a string art design. She has positioned ten nails, similar to
the vertices of a decagon, onto a board. How many strings will she need to
interconnect all vertices of the design?

A. 20
B. 70
C. 35
D. 45
Answer

181