advanced geometry section 2.5 addition and subtraction properties

Advanced Geometry

Section 2.5 Addition and Subtraction Properties

Learner Objective: Students will apply the addition and subtraction  properties of segments and angles.

Learner Objective: Students will apply the addition and subtraction properties of sebments and 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 anglethen 90 - x = complement of the angleand 180 - x = supplement of the angle

so 90 - x = 180 - x - 40 +x +x 90 = 140 !

NotPossible

Solution

Page 3: Advanced Geometry Section 2.5 Addition and Subtraction Properties

What is true about AB and CD?What is true about AC and BD?

Then what conclusion can we draw?

Page 4: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If FG ≅ HE, what can we say about FH and GE?

Page 5: Advanced Geometry Section 2.5 Addition and Subtraction Properties

Theorem:If the same segment is added to congruent segments,then the sums are congruent. (Addition Property)

Proof:

Page 6: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If AB ≅ FG and BD ≅ GE, what do we know about AD and FE?

Page 7: Advanced Geometry Section 2.5 Addition and Subtraction Properties

Theorem:If congruent segments are added to congruent segments,then the sums are congruent. (Addition Property)

Proof:

Page 8: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If ABE ≅ DBC, what do we know about ABD and EBC? Why?

Page 9: Advanced Geometry Section 2.5 Addition and Subtraction Properties

Theorem:If the same angle is added to congruent angles,then the sums are congruent. (Addition Property)

Proof:

Page 10: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If BAC ≅ GFH and CAD ≅ HFE,what else do we know? Why?

Page 11: Advanced Geometry Section 2.5 Addition and Subtraction Properties

Theorem:If congruent angles are added to congruent angles,then the sums are congruent. (Addition Property)

Proof:

Page 12: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If FH ≅ GE, what can we say about FG and HE? Why?

Page 13: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If ABD ≅ EBC, what do we know about ABE and DBC? Why?

Page 14: Advanced Geometry Section 2.5 Addition and Subtraction Properties

Theorem:If the same segment (or angle) is subtracted from congruent  segments (or angles),then the differences are congruent. (Subtraction Property)

Proof:

Page 15: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If AB ≅ FG and AD ≅ FE, what do we know about BD and GE?

Why?

Page 16: Advanced Geometry Section 2.5 Addition and Subtraction Properties

If BAC ≅ GFH and BAD ≅ GFE,what else do we know? Why?

Page 17: Advanced Geometry Section 2.5 Addition and Subtraction Properties

Theorem:If congruent segments (or angles) are subtracted from congruent  segments (or angles),then the differences are congruent. (Subtraction Property)

Proof:

Page 18: Advanced Geometry Section 2.5 Addition and Subtraction Properties

Using the Addition and Subtraction Properties in Proofs.

1. An addition property is used when the segments or  angles in the conclusion are greater then those in the  given information.2. A subtraction property is used when the segments or  angles in the conclusion are smaller than those in the  given information.