B Apply

Use the given property to complete each statement.

14. Symmetric Property of Equality

    If A B = Y U , eh b equals y u comma  then ? ¯ . modified question mark with under bar below , .

15. Symmetric Property of Congruence

    If ∠ H ≅ ∠ K , angle h , approximately equal to , angle k , comma  then ? ¯ ≅ ∠ H . modified question mark with under bar below , approximately equal to , angle h , .

16. Reflexive Property of Congruence

    ∠ P O R ≅ ? ¯ angle p o r approximately equal to , modified question mark with under bar below

17. Distributive Property

    3 ( x − 1 ) = 3 x − ? ¯ 3 open x minus 1 close equals 3 x minus , modified question mark with under bar below

18. Substitution Property

    If L M = 7 l m equals 7  and E F + L M = N P , e f plus l m equals n p comma

    then ? ¯ = N P . modified question mark with under bar below , equals n p .

19. Transitive Property of Congruence

    If ∠ X Y Z ≅ ∠ A O B angle x y z approximately equal to angle eh o b  and

    ∠ A O B ≅ ∠ W Y T , angle eh o b approximately equal to angle w y t comma  then ? ¯ . modified question mark with under bar below , .

20. Think About a Plan A very important part in writing proofs is analyzing the diagram for key information. What true statements can you make based on the diagram below?
    • What theorems or definitions relate to the geometric figures in the diagram?
    • What types of markings show relationships between parts of geometric figures?

    

21. Writing Explain why the statements L R ¯ ≅ R L ¯ l r bar , approximately equal to , r l bar  and ∠ C B A ≅ ∠ A B C angle c b eh approximately equal to angle eh b c  are both true by the Reflexive Property of Congruence.

22. Reasoning Complete the following statement. Describe the reasoning that supports your answer.

    The Transitive Property of Falling Dominoes: If Domino A causes Domino B to fall, and Domino B causes Domino C to fall, then Domino A causes Domino ? ¯ modified question mark with under bar below  to fall.

Write a two-column proof.

Proof

23. Given: K M = 35 k m equals 35

    Prove: K L = 15 k l equals 15

    

24. Proof

    Given: m ∠ G F I = 128 m angle g f i equals 128

    Prove: m ∠ E F I = 40 m angle e f i equals 40

    

C Challenge

25. Error Analysis The steps below “show” that 1 = 2 . 1 equals , 2 .  Describe the error.

    a = b Given a b = b 2 Multiplication Property of Equality  a b − a 2 = b 2 − a 2 Subtraction Property of Equality  a ( b − a ) = ( b + a ) ( b − a ) Distributive Property  a = b + a Division Property of Equality  a = a + a Substitution Property  a = 2 a Simplify. 1 = 2 Division Property of Equality  table with 8 rows and 3 columns , row1 column 1 , eh equals , column 2 b , column 3 cap given , row2 column 1 , eh b equals , column 2 b squared , column 3 cap multiplicationcap propertyofcap equality , row3 column 1 , eh b minus , eh squared , equals , column 2 b squared , minus , eh squared , column 3 cap subtractioncap propertyofcap equality , row4 column 1 , eh open b minus eh close equals , column 2 open b plus , eh close open b minus eh close , column 3 cap distributivecap property , row5 column 1 , eh equals , column 2 b plus , eh , column 3 cap divisioncap propertyofcap equality , row6 column 1 , eh equals , column 2 eh plus , eh , column 3 cap substitutioncap property , row7 column 1 , eh equals , column 2 2 eh , column 3 cap simplify. , row8 column 1 , 1 equals , column 2 2 , column 3 cap divisioncap propertyofcap equality , end table

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