Download Geometry Unit 2 Learning Targets

Course: Geometry
Chapter 2: Geometric Reasoning
Big Idea: Study inductive and deductive reasoning. Use conditional and biconditional statements.
Write two-column, flow and paragraph proofs.
Learning Target: I CAN
2-1a … Use inductive
reasoning to identify patterns
and make conjectures
Example
Find the next item in the pattern.
1. 100, 81, 64, 49, …
2.
Alabama, Alaska, Arizona, …
Complete the conjecture.
3. The square of any negative number is:
4.
The number of segments determined by n points is:
2-1b. … Find
counterexamples to disprove
conjectures
Show that each conjecture is false by finding a counterexample.
1. For any integer n, n3 > 0
2. Each angle in a right triangle has a different measure
2-2a. … Identify, write and
analyze the truth value of
conditional statements
4.7
Identify the hypothesis and conclusion of the conditional.
1. If you can see the stars, then it is night.
2. A pencil writes well if it is sharp.
2-2b. … Write the inverse,
converse and contrapositive
of a conditional statement
2-3. … Apply the Law of
Detachment and Law of
Syllogism in logical
reasoning
Determine if each conditional is true. If false, give a counterexample.
3. If two points are collinear, then a right triangle contains one obtuse angle.
4. If a living thing is green, then it is a plant.
Write the converse, inverse and contrapositive:
If an animal is an armadillo, then it is nocturnal.
Determine if the conjecture is valid by the Law of Detachment.
1. Given: An obtuse triangle has two acute angles. Triangle ABC is obtuse.
Conjecture: Triangle ABC has two acute angles.
Determine if the conjecture is valid by the Law of Syllogism.
2. Given: The radio is distracting when I am studying.
If it is 7:30 PM on a weeknight, I am studying.
Conjecture: If it is 7:30 PM on a weeknight, the radio is distracting.
3. Given: No human is immortal. Fido the dog is not human.
Conjecture: Fido the dog is immortal.
Starting
Getting
There
Got It
Learning Target: I CAN
2-4. … Write and analyze
biconditional statements
Example
Starting
Write the converse and a biconditional statement for the following:
1. Conditional: An angle is obtuse when it measures between 90o and 180o
For the conditional, write the converse and a biconditional statement.
2. Conditional: If n is an odd number, then n-1 is divisible by 2.
Write each definition as a biconditional.
3. A cube is a three-dimensional solid with six square faces.
2-5a. … Review properties of
equality and use them to write
algebraic proofs
:
Write the property demonstrated by each statement:
1. If a = b, then ac = bc
2. a(b + c) = ab + ac
2-5b…. Identify properties of
equality and congruence
Solve the equation. Show all steps and write a justification for each step.
3. t + 6.5 = 3t – 1.3
Write the property demonstrated by each statement:
1. If SPR  MLN and MLN  DGY , then
SPR  DGY
2. If ABC  DEF , then DEF  ABC
Solve the problem. Write justifications for each step in your solution.
3. Solve for m<ZYX in terms of m<CBD.
Given:  XYZ  ABC
2-6…. Write two column
proofs
BD is the angle bisector of <ABC.
Write a two-column proof.
1. Given: The sum of the angle measures in a triangle is 180 o
Prove: m<1 = m<3 + m<4
3
1
2-7…. Write flowchart and
paragraph proofs
Re-write the given proof as a flowchart and paragraph proof.
1. Given:  4  3
Prove: m<1 = m<2
1
1
Statements
1. <1 and < 4 are supplementary
2.
3.
 4  3
 1  2
4.
m<1 = m<2
Reasons
1. Linear Pair
Theorem
2. Given
3.  Supps.
Theorem
4.Def. of  angles
2
3
2
4
4
Getting
There
Got It