Page 191 - Math Course 2 (Book 2)

Postulates and Paragraph Proofs

Let’s Begin Your Turn!

Write a Paragraph Proof

Given RT ≅ TY, S is the midpoint of RT, and X is the
Write a Paragraph Proof
midpoint of TY, a paragraph proof to show that
Example ST ≅ TX has been provided with one reason
missing,Choose the best reason to complete the
proof.
Given AC intersects CD, write a paragraph proof to
show that A, C, and D determine a plane.
Given: AC intersects CD.

Prove: ACD is a plane.
CD
AC
Proof: and must intersect at C because if
two lines intersect, then their intersection is exact-
AC
ly one point (12.6) . Point A is on and point D is
on . Points A, C, and D are not collinear. There-
CD
fore, ACD is a plane as it contains three points not We are given that S is the midpoint of RT and X is
on the same line (12.4). the midpoint of TY. By ? RS ≅ ST and TX ≅ XY.

Using the definition of congruent segments,
12.4 A plane contains at least three points not on
the same line. RS = ST and TX = XY. Also using the given state-

12.6 If two lines intersect, then their intersection ment RT ≅ TY and the definition of congruent
1
1
is exactly one point. segments, RT = TY. If RT = TY, then RT = TY.
2
2
1
1
Since S and X are midpoints, RT = ST and TY
2 2
= TX. By Substitution, ST = TX and by definition of
congruence, ST ≅ TX
A. Definition of midpoint
B. Segment Addition Postulate
C. Definition of congruent segments
D. Substitution

Answer

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