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Addition, Subtraction, Multiplication, and Division Properties

2.5 & 2.6

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Learning Target & Do Now

LT: By the end of class, I will understand the geometric theorems related to the properties of addition, subtraction, multiplication, and division.

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DN: Three angles sum to 270°. The first angle is fourth fifths the size of the second, which is half of fifteen more than the third. What are the values of the angles?

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Addition and Subtraction Properties

AB ≅ CD

What happens if I add EF to both?

AB + EF ≅ CD + EF

If we were to subtract?

AB - EF ≅ CD - EF

A

C

B

D

E

F

A

B

C

D

E

F

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Addition Theorems (Addition Property)

8. If a segment is added to two congruent segments, the sums are congruent.

9. If an angle is added to two congruent angles, the sums are congruent.

10. If congruent segments are added to congruent segments, the sums are congruent.

11. If congruent angles are added to congruent angles, the sums are congruent.

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Subtraction Theorems (Subtraction Property)

12. If a segment or angle is subtracted from congruent segments or angles, the results are congruent.

13. If congruent segments or angles are subtracted from congruent segments or angles, the results are congruent.

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Example

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Multiplication and Division Theorems

14. If segments or angles are congruent, their like multiples are also congruent (Multiplication Property)

15. If segments or angles are congruent, their like divisions are congruent (Division Property)

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These are particularly useful with bisectors and trisectors!

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You Do