2.3 Writing Proofs

Proof #1

Practice 2.3: Writing Proofs

Support each statement by writing a conclusion with a valid reason.

1. Given:

2x = 72

2. Given:

. 3.

Given:

X is the midpoint of

Conclusion: __x__=_3__6__________

Reason:___D_i_v_is_io_n__P_r_o_p_e_r_t_y

Conclusion: A_n_g_le_s__A__a_n_d__B are Conclusion:

__D_X__=_X_R_______

congruent

Reason:_________________

Reason:__D_e_f__o_f _m_i_d_p_t_____

All Right Angles are Congruent

Directions: Complete the following proofs.

Given: 10x + 4 = 44

Statement

1. 10x + 4 = 44 2. 10x = 40 3. x=4

Prove: x = 4

Reason

1. Given 2. Subtraction Property 3. Division Property

Given: 10x + 42 = 20 ? x

Prove: x = -2

Statement

Reason

1. 10x + 42 = 20 - x 1. Given

2. 11x + 42 = 20

2. Addition Property

3. 11x = -22

3. Subtraction Property

4. x = -2

4. Division Property

Proof #4

Proof #2

Given: 1 - x = 11

Statement

1. 1 - x = 11 2. -x = 10 3. x = -10

Prove: x = 0

Reason

1. Given 2. Subtraction Property 3. Mult/Div Property

Given: 6x - (4x ? 1) = 2

Statement

1. 6x - (4x - 1) = 2

2. 6x - 4x + 1 = 2 3. 2x + 1 = 2

4.

2x = 1

5. x = 1/2

Prove: x = ?

Reason

1. Given 2. Distributive Property 3. Combine Like Terms 4. Subtraction Property 5. Division Property

Proof #3

Proof #5

Given: 13 ? 4(x ? 2) - 41 = 0

Statement

1. 13 - 4(x - 2) - 41 = 0

2. -28 - 4(x - 2) = 0 3. -4(x - 2)= 28

4.

x - 2 = -7

5.

x = -5

6.

Prove: x = -5

Reason

1. Given 2. Combine Like Terms 3. Addition Property 4. Division property (Div by -4) 5. Addition Property 6.

There are other correct proofs for #5 possible....

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