Advanced Geometry Section 2 5 Addition and Subtraction

Advanced Geometry Section 2. 5 Addition and Subtraction Properties Learner Objective: Students will apply the addition and subtraction and angles. roperties of segments

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Opener: If the complement of an angle is 40 less than the supplement of the angle, find the measure of the angle. Let x = the angle then 90 - x = complement of the angle and 180 - x = supplement of the angle Solution so 90 - x = 180 - x - 40 +x +x 90 = 140 ! Not Possible

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. What is true about AB and CD? What is true about AC and BD? Then what conclusion can we draw?

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If FG ≅ HE, what can we say about FH and GE?

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Theorem: If the same segment is added to congruent segments, then the sums are congruent. (Addition Property) Proof:

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If AB ≅ FG and BD ≅ GE, what do we know about AD and FE?

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Theorem: If congruent segments are added to congruent segments, then the sums are congruent. (Addition Property) Proof:

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If ABE ≅ DBC, what do we know about EBC? Why? ABD and

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Theorem: If the same angle is added to congruent angles, then the sums are congruent. (Addition Property) Proof:

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If BAC ≅ GFH and CAD ≅ what else do we know? Why? HFE,

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Theorem: If congruent angles are added to congruent angles, then the sums are congruent. (Addition Property) Proof:

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If FH ≅ GE, what can we say about FG and HE? Why?

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If ABD ≅ EBC, what do we know about DBC? Why? ABE and

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Theorem: If the same segment (or angle) is subtracted from congruent egments (or angles), then the differences are congruent. (Subtraction Property) Proof:

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If AB ≅ FG and AD ≅ FE, what do we know about BD and GE? Why?

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. If BAC ≅ GFH and BAD ≅ what else do we know? Why? GFE,

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Theorem: If congruent segments (or angles) are subtracted from congruent egments (or angles), then the differences are congruent. (Subtraction Property) Proof:

Learner Objective: Students will apply the addition and subtraction properties of sebments nd angles. Using the Addition and Subtraction Properties in Proofs. 1. An addition property is used when the segments or ngles in the conclusion are greater then those in the iven information. 2. A subtraction property is used when the segments or ngles in the conclusion are smaller than those in the iven information.