Download Chapter 2 Study Guide Things to know/ be able to do There will be 2

Chapter 2 Study Guide
Things to know/ be able to do
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There will be 2 proofs that you must fill in. They will come from sections 6 or 7.
They can be in two-column format, flowchart proof format, or paragraph proof
format. There will be a word bank. The options are:
o Vertical Angles Theorem
o Congruent Complements Theorem
o Congruent Supplements Theorem
o Linear Pair Theorem
o Common Segments Theorem
Justify steps of solving an algebraic equation (section 5)
Write conditional statements, converses, and biconditional statements from a
sentence
Give a SPECIFIC counterexample to a false statement
Determine if a statement is a good definition and justify your answer
Practice Problems
For problems #1 – 2, justify each step by writing the property used.
1.
Segment Addition Postulate
Substitution Property of Equality
Combine Like Terms
Subtraction Property of Equality
Division Property of Equality
2.
Angle Addition Postulate
Substitution Property of Equality
Combine Like Terms
Addition Property of Equality
Division Property of Equality
For problems #3 – 6, state the property that justifies each statement.
3.
4,
5.
6.
Symmetric Property of Congruence
Transitive Property of Congruence
Symmetric Property of Equality
Reflexive Property of Congruence
For problems # 7 – 10, write the conditional statement and converse of each
statement. If the statement is a good definition, write the biconditional statement. If
the statement is not a good definition, then give a counterexample.
7. A polygon with exactly 8 sides is an octagon.
Conditional: If a polygon has exactly 8 sides, then it is an octagon.
Converse: If a polygon is an octagon, then it has exactly 8 sides.
Biconditional/counterexample: A polygon is an octagon if and only if it has
exactly 8 sides.
8. An isosceles triangle has 2 congruent sides.
Conditional: If a triangle is isosceles, then it has 2 congruent sides.
Converse: If a triangle has 2 congruent sides, then it is isosceles.
Biconditional/counterexample: A triangle is isosceles if and only if it has 2
congruent sides.
9. A square is a quadrilateral with 4 congruent sides.
Conditional: If a quadrilateral is a square, then it has 4 congruent sides.
Converse: If a quadrilateral has 4 congruent sides, then it is a square.
Biconditional/counterexample: False, a rhombus has 4 congruent sides but
doesn’t have to have 4 right angles, which means it is not a square.
10. Angles whose measures add up to 90o are complementary.
Conditional: If the measures of some angles add up to 90o, then the angles are
complementary.
Converse: If the angles are complementary, then the measures add up to 90 o.
Biconditional/counterexample: False, they needed to specify a PAIR of angles.
20o, 30o, and 40o add up to 90o but are not complementary.
11. Look up the vertical angles theorem proof in section 6 or section 7 and rewrite it as a
paragraph proof.
See the classwork review from Wednesday for a proof of the vertical angles theorem.
12. Look up the linear pair theorem proof in section 6 and rewrite it as a flowchart proof.
See the classwork review from Wednesday for a proof of the linear pair theorem.
Complete each proof by filling in the blanks from the word bank between the proofs.
∠4 𝑎𝑛𝑑 ∠5 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦
𝑔𝑖𝑣𝑒𝑛
𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑎𝑛𝑔𝑙𝑒𝑠
𝑚∠5 + 𝑚∠6 = 180
𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑣𝑒 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦
𝑚∠4 = 𝑚∠5
∠4 ≅ ∠5
𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡 𝑎𝑛𝑔𝑙𝑒𝑠
Given
Definition of right angle
Definition of congruent angles
Definition of supplementary angles
Transitive Property of Equality
Transitive Property of Equality
∠1 𝑎𝑛𝑑 ∠2 𝑎𝑟𝑒 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒𝑠
𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒
𝑚∠2 = 90
𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑣𝑒 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦
∠1 ≅ ∠2