Geometry Reasoning and Proof

Patterns and Inductive Reasoning

100

The next two terms in the sequence of 1,3,5,8,11,15,19,24, ______, _______

What is 29, 35

200

The next term in the sequence of 1/2, 2/6,3/18,4/54, ____

What is 5/162

300

A counter example for the following statement: The sum of two integers is always positive.

What is -13 + 2

400

Double Jeopardy.......Find the sum of the first 10 consecutive whole numbers....

What is 55

500

Provide a counterexample for: All states in the United States share a border with another state.

What is Hawaii or Alaska?

Conditional Statements

100

Identify the hypothesis and conclusion of the following conditional statement. If the sidewalks are wet, then it has been raining.

What is the sidewalks are wet and it has been raining

200

Determine if the conditional statement is true or false..if false provide a counter example If the figure has four congruent angles, then the figure is a square.

What is a rectangle

300

Write the converse of the following conditional: If the temperature outside is below freezing, then ice can form on the sidewalks.

What is ..if ice can form on the sidewalks, then the temperature outside is below freezing.

400

Write the contrapositive of the following conditional: If the shoe fits, then you can wear it.

What is if you can't wear it, then the shoe does not fit.

500

Given the following conditional: If it is snowing then it is cloudy.... The following statement is the converse, inverse, or contrapositive.... If it is not snowing then it is not cloudy.

What is converse

Laws and Definitions

100

Angle A is congruent to angle B

And angle B is congruent to angle C

What other two angles are congruent and what property?

angle A is congruent to angle C by transitive property.

200

For Law of Syllogism, If P-->Q, and Q-->R,

Then P-->R.

300

For Law of Detachment, If P-->Q, and P is true.

Then Q is true.

400

State whether the following argument uses Law of Detachment or Law of Syllogism; If it's Friday, then Kendra's family has pizza for dinner, today is Friday, therefore Kendra's family will have pizza for dinner.

Law of Detachment.

500

Determine if statement 3 follows from statements 1&2. Provide a counterexample 

(1) Vertical angles are congruent

(2) <A ≅ <B

(3) <A ≅ <B are vertical angles

invalid 

Law of Syllogism or Detachment

100

Make a conclusion if possible...

 If cats prowl, mice will scatter. Mice are scattering

What is cannot conclude

200

Make a conclusion if possible. 

To take Calculus, you must first take Algebra II. To take Algebra II, you must first take Algebra I.

What is To take Calculus you must first take Algebra I

300

Make a conclusion if possible, state the law used.

 If you pass the road test then you will get your driver's license. Samantha passed the road test.

 Samantha will get her driver's license..law of detachment

400

State whether the following argument uses Law of Detachment or Law of Syllogism; If it's Friday, then Kendra's family has pizza for dinner, today is Friday, therefore Kendra's family will have pizza for dinner.

Law of Detachment.

500

Write the following statement using the law of syllogism; If the sun is shining, then it's a beautiful day. If it's a beautiful day, then we'll have a picnic.

If the sun is shining, then we'll have a picnic.

Proofs

100

By the Transitive Property, If Segment XY ≅ Segment CF, and Segment CF ≅ Segment DH...

Segment XY ≅ Segment DH

200

By the Segment Addition Postulate, Segment DF+ Segment FG=?

Segment DG

300

What is the next step in this equation?

 1. 12w-4w=6.       Given 

2. 8w=6.        Subtraction property of equality 

3.________     _____________. ?

3. w=3/4. 3. Division property of equality

400

Solve the following using a two-column proof using 4(3x+12)=2x-28

Statements:1)4(3x+12)=2x-28, 2)12x+48=2x-28, 3)10x=-76, 4)x=-7.6 Reasons:1)Given, 2)Distributive Property, 3)Subtraction Property of Equality, 5) Division Property of Equality

500

double jeopardy

What is What is see board