Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK
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Part IV<br />
For each question, use <strong>the</strong> specific criteria to award a maximum of 6 credits.<br />
18 Score Explanation<br />
6 The following proof or ano<strong>the</strong>r appropriate proof is given.<br />
Statements Reasons<br />
1. −−−<br />
DA −−<br />
AB , −−−<br />
DC −−<br />
CB 1. Given.<br />
2. BAD and BCD are right angles. 2. Definition of perpendicular lines.<br />
3. BAD BCD 3. Right angles are congruent.<br />
4. 1 2 4. Given.<br />
5. BAE BCE 5. Subtraction postulate.<br />
6. −−<br />
BD −−<br />
AC at E 6. Given.<br />
7. BEA and BEC are right angles. 7. Definition of perpendicular lines.<br />
8. BEA BEC 8. Right angles are congruent.<br />
9. −−<br />
BE −−<br />
BE 9. Reflexive property of congruence.<br />
10. ABE CBE 10. AAS AAS.<br />
11. 3 4 11. CPCTC.<br />
5 An appropriate proof with correct conclusion is shown, but one reason is faulty and/<br />
or one statement is missing.<br />
4 A faulty conclusion or no conclusion is drawn from <strong>the</strong> statements and reasoning.<br />
3 An appropriate proof with correct conclusion is shown, but two reasons are faulty or<br />
two steps are missing.<br />
2 An appropriate proof with correct conclusion is used, but more than two reasons are<br />
faulty or more than two steps are missing or have errors.<br />
1 3 4 and a reason is given, but no appropriate method is shown.<br />
0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct<br />
response that was obtained by an obviously incorrect procedure.<br />
19 Score Explanation<br />
2 a Student proves that MIKE is a rhombus by showing that<br />
MI IK KE EM √ 40 or by some o<strong>the</strong>r appropriate method.<br />
1 a The correct conclusion is reached and a reason is given, but no appropriate method<br />
is shown.<br />
2 b Student shows that MIKE is not a square by showing that <strong>the</strong><br />
diagonals are not perpendicular. Slope −− <br />
1<br />
MI _ and <strong>the</strong> slope<br />
3 −− 3.<br />
IK<br />
1 b The correct conclusion is reached and a reason is given, but no appropriate method<br />
is shown.<br />
2 c 32, and an appropriate explanation is given.<br />
1 c 32, but no appropriate explanation is given.<br />
0 A zero response is completely incorrect, irrelevant, or incoherent or is a correct response<br />
that was obtained by an obviously incorrect procedure.<br />
Chapters 1–11 125