Advanced Geometry Section 1 4 Beginning Proofs Learner

Advanced Geometry Section 1. 4 Beginning Proofs Learner Objective: Students will write simple two column proofs.

Learner Objective: Students will write simple two-column proofs. Is S STR a right angle? Justify your response. 120 - 3 x E 60 + 3 x T R

Learner Objective: Students will write simple two-column proofs. The type of proof we will use most often in this course is the “Two-Column” proof. In a two column proof, the left hand column contains a list of steps in an argument that begins with known or given information and ends with the conclusion we wish to prove. For each step (statement) in the left hand column, we must supply a reason or justification in the right hand column. These reasons cannot just be things we make up. Valid reasons include: efinitions that we have already learned. reviously stated and proven Theorems. reviously stated Postulates. athematical operations. ivens alid Assumptions

Learner Objective: Students will write simple two-column proofs. At this point in the course, we have covered the following definitions: f an angle is an Acute Angle, hen its measure is greater than 0° and less than 90°. Trigger Conclusion or If an angle's measure is greater than 0° and less than 90° hen it is an Acute Angle. If an angle is a Right Angle, hen its measure is 90°. Trigger Conclusion or If an angle measures 90°, hen it is a Right Angle. Trigger Conclusion

Learner Objective: Students will write simple two-column proofs. If an angle is an Obtuse Angle, then its measure is greater than 90° and less than 180°. Trigger Conclusion or an angle's measure is greater than 90° and less than 180°, then it is an Obtuse Angle. If If an angle is a Straight Angle, then its measure is 180°. Trigger Conclusion or an angle measures 180°, then it is a Straight Angle. If Trigger Conclusion

Learner Objective: Students will write simple two-column proofs. If two angles are Congruent Angles, then they have the same measure. Trigger Conclusion or two angles have the same measure, then they are Congruent Angles. If If two segments are Congruent Segments, then they have the same measure. Trigger Conclusion or two segments have the same measure, then they are Congruent Segments. If Trigger Conclusion

Learner Objective: Students will write simple two-column proofs. All of the above definitions can be used as reasons in a proof. In addition, the following can also be used: Given Assumed: traight Lines and Straight Angles ollinearity of points etweenness of points elative positions of points Addition Subtraction Multiplication Division Substitution

Learner Objective: Students will write simple two-column proofs. A theorem is a mathematical statement that can be proved. A postulate is a mathematical statement that cannot be proved. When a theorem is presented in this course, we will first prove theorem. Once theorem has been proved, we can then use this theorem to help prove homework problems. These theorems will also be used later to prove more advanced theorems.

Learner Objective: Students will write simple two-column proofs. OUR FIRST THEOREMS! Theorem: If two angles are both right angles, then they are congruent. (First we will draw a diagram that represents the condition “If two angles are right angles”. We will state a “Given” based upon this condition and will then state a “Prove” based upon the conclusion “then they are congruent”. ) Given: is a right Angle Prove: A B

Learner Objective: Students will write simple two-column proofs. Theorem: If two angles are both right angles, then they are congruent. PROOF: Given: is a right Angle Prove: A B

Learner Objective: Students will write simple two-column proofs. Theorem: If two angles are both right angles, then they are congruent. PROOF: Given: is a right Angle starts with “given” information or with a valid assumption based upon the diagram Prove: A B

Learner Objective: Students will write simple two-column proofs. Theorem: If two angles are both right angles, then they are congruent. PROOF: Given: is a right Angle Prove: A B Before using a “reason”, the condition of the statement must have already been shown to be true

Learner Objective: Students will write simple two-column proofs. ends with the “Prove” statement Theorem: If two angles are both right angles, then they are congruent. PROOF: Given: is a right Angle Prove: A B The conclusion of each "reason" must match the statement made on that line.

Learner Objective: Students will write simple two-column proofs. ends with the “Prove” statement Theorem: If two angles are both right angles, then they are congruent. PROOF: Given: is a right Angle Prove: A B ends with the “Prove” statement