Proofs
Check out the interactive quiz, Chapter
2, “Videos & Activities”.
Also see page S82+ for complete
listing of theorems, postulates, etc.
OR use your “cheat sheet”!
KL  MN and
KLM 
MNK.
Determine if the quadrilateral must be a parallelogram. Justify
your answer.
a.
No. Only one set of angles and sides are given as congruent. The
conditions for a parallelogram are not met.
b.
Yes. Opposite angles are congruent to each other. This is sufficient
evidence to prove that the quadrilateral is a parallelogram.
c.
Yes. Opposite sides are congruent to each other. This is sufficient
evidence to prove that the quadrilateral is a parallelogram.
d.
Yes. One set of opposite sides are congruent, and one set of
opposite angles are congruent. This is sufficient evidence to prove that the
quadrilateral is a parallelogram.
Which of these could BEST be used to demonstrate the
vertical angle theorem?
a.
b.
scissors
thermometer
c.
d.
drawing compass
protractor
For a homework assignment about quadrilaterals inscribed in a circle,
Gloria drew the diagram shown below.
She wrote the following step in a proof.
m S
1
2
mPQR and m Q 
1
2
mPSR
because the measure of an angle inscribed in a circle is one-half the
measure of the intercepted arc.
Based on this diagram and the beginning of Gloria’s proof, which of the
following is a true conclusion that Gloria could prove?
a. The opposite angles of an inscribed quadrilateral are congruent.
b. The opposite angles of an inscribed quadrilateral are right angles.
c. The opposite angles of an inscribed quadrilateral are complementary.
d. The opposite angles of an inscribed quadrilateral are supplementary.
Given: AB GH; AC
FH; AC  FH
Prove: ABC  HGF
a. 1. Alternate Exterior Angles Theorem
2. Alternate Interior Angles Theorem
c. 1. Alternate Exterior Angles Theorem
2. Alternate Exterior Angles Theorem
b. 1. Alternate Interior Angles Theorem
2. Alternate Exterior Angles Theorem
d. 1. Alternate Interior Angles Theorem
2. Alternate Interior Angles Theorem
Write a justification for each step to prove EF = GH, given that EG = FH.
Identify the property that justifies the statement:
AB  CD and CD  EF so AB  EF
a.
b.
c.
d.
Reflexive Property of Congruence
Symmetric Property of Congruence
Substitution Property of Congruence
Transitive Property of Congruence