Download Name: Chapter 2 Honors Geometry Section 2.1

Name: ____________________________
Honors Geometry
Chapter 2
Section 2.1-2.3 Practice
Describe a pattern in the numbers. Write the next number in the pattern.
1. a)
1 3 5 7
, , , ,
3 4 5 6
𝟗
𝟕
b) 2, 5, 11, 23, 47
Numerator is consecutive odd integers
Add twice the previous number that was added,
Denominator – add one to the previous denominator
starting with 3
Make a conjecture about each value or geometric relationship.
2. The relationship between AP and PB if M is the midpoint of AB and P is the midpoint of AM.
̅̅̅̅
𝑃𝐵 𝑖𝑠 𝑡ℎ𝑟𝑒𝑒 𝑡𝑖𝑚𝑒𝑠 𝑎𝑠 𝑙𝑜𝑛𝑔𝑠 𝑎𝑠 ̅̅̅̅
𝐴𝑃
A
P
M
B
3. The product of three negative numbers.
Will be a negative number
Decide whether each conjecture is true or false. If false, find a counterexample.
4. The quotient of two whole numbers is a whole number.
False
2
4
= .5 and .5 is not a whole number
5. The square root of a number x is always less than x.
False
1
1
1
1
√ = and <
4 2
4
2
6. If a ray intersects a segment at its midpoint, then the ray is perpendicular to the segment.
False
Determine if Statement 3 follows from the Statements 1 and 2 by either the Law of Detachment or Law of
Syllogism. If it does, state which law was used. If it does not, write invalid.
7. (1) If an angle measures less than 90°, then it is not obtuse.
(2) 𝑚∠𝐴𝐵𝐶 = 85°
(3) ∠𝐴𝐵𝐶 is not obtuse.
Law of Detachment
8. (1)All 95° angles are congruent.
(2) ∠𝐴 ≅ ∠𝐵
(3) ∠𝐴 and ∠𝐵 are 95°angles.
Invalid
9. (1)If ∠2 is acute, then ∠3 is obtuse.
(2) If ∠3 is obtuse, then ∠4 is acute.
(3) If ∠2 is acute, then ∠4 is acute.
Law of Syllogism
Given the following statements, state a conclusion and which law is used.
10. If you order the meatloaf, then it will be served with mashed potatoes. Matthew ordered the meatloaf.
It will be served with mashed potatoes.
Law of Detachment
11. If you go to the hockey game, then you like hockey. If you like hockey, then you support the hockey team.
If you go to the hockey game, then you support the hockey team.
Law of Syllogism
12. If you eat too much candy, then you will get sick. Ellen got sick.
Invalid – no conclusion can be made
13. If an angle is not right, then its measure is between 0° and 90°. A is not right.
Invalid – the original conditional statement is false
Determine whether or not the given conditional and its converse are true. Use this information to write a
biconditional statement if it is appropriate. If not, explain why it is not appropriate.
14. If it is Wednesday, then it is not Thursday. True
Converse: If it is not Thursday, then it is Wednesday. False
If it is not Thursday it could be any other day of the week.
15. If two lines intersect to form a right angle, then they are perpendicular. True
If two lines are perpendicular, then they intersect to form a right angle. True
Two lines are perpendicular IFF they intersect to form a right angle.
Write the biconditional as a conditional and its converse. Then determine whether the biconditional is true or
false. If false, give a counterexample.
16. Two angles are supplementary if and only if the sum of their measures is 180°. True
Conditional: If two angles are supplementary, then the sum of their measures is 180°.
Converse: If two angles have a sum of 180°, then they are supplementary angles.
Rewrite the following statement as a conditional and its converse. If the converse is true, write its biconditional.
If the converse is false, provide a counterexample.
17. Complementary angles are two angles whose measures sum up to 90°.
Conditional: If two angles are complementary, then the sum of their measures is 90°.
Converse: If two angles have a sum of 90°, then they are complementary.
True
Biconditional: Two angles are complementary IFF the sum of their measures is 90°.
Rewrite the following statement as a conditional and its converse. If the converse is true, write its biconditional.
If the converse is false, provide a counterexample.
18. Vertical angles are congruent.
Conditional: If two angles are vertical, then they are congruent.
Converse: If two angles are congruent, then they are vertical. False