Skills Practice - Mrs. Foy's Classroom

NAME DATE PERIOD
2-1
Write a conjecture that describes the pattern in the sequence. Then use your
conjecture to find the next item in the sequence.
1.
Skills Practice
Inductive Reasoning and Conjecture
2. -4, -1, 2, 5, 8 3. 6, −
11
2 , 5, −
9 , 4 4. -2, 4, -8, 16, -32
2
Make a conjecture about each value or geometric relationship.
5. Points A, B, and C are collinear, 6. Point P is the midpoint of NQ
−−−
and D is between B and C.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. ∠1, ∠2, ∠3, and ∠4 form four 8. ∠3 ∠4
linear pairs.
Determine whether each conjecture is true or false. Give a counterexample for
any false conjecture.
9. If ∠ ABC and ∠ CBD form a linear pair, then ∠ ABC ∠ CBD.
10. If −− AB , −− BC , and −− AC are congruent, then A, B, and C are collinear.
11. If AB + BC = AC, then AB = BC.
12. If ∠1 is complementary to ∠2, and ∠1 is complementary to ∠3, then ∠2 ∠3.
Chapter 2 15 Glencoe Geometry

NAME DATE PERIOD
2-1 Practice
Inductive Reasoning and Conjecture
Make a conjecture about the next item in each sequence.
1.
1
2. 5, -10, 15, -20 3. -2, 1, - −
2 , −
1 4 , - −
1
8
4. 12, 6, 3, 1.5, 0.75
Make a conjecture about each value or geometric relationship.
5. ∠ABC is a right angle. 6. Point S is between R and T.
7. P, Q, R, and S are noncollinear 8. ABCD is a parallelogram.
and −−− PQ −−− QR −− RS −− SP .
Determine whether each conjecture is true or false. Give a counterexample for
any false conjecture.
9. If S, T, and U are collinear and ST = TU, then T is the midpoint of −−− SU .
10. If ∠1 and ∠2 are adjacent angles, then ∠1 and ∠2 form a linear pair.
11. If −−− GH and −− JK form a right angle and intersect at P, then −−− GH ⊥ −− JK .
12. ALLERGIES Each spring, Rachel starts sneezing when the pear trees on her street blossom.
She reasons that she is allergic to pear trees. Find a counterexample to Rachel’s conjecture.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 2 16 Glencoe Geometry