PROOF FORMATS: THE PLAN OF THE PROOF

In the six essential parts of a two-column proof, the proof comes after the

Plan of the Proof

Match the reasons with the statements. GIVEN: x² + 6x + 2x + 12 = 0 TO PROVE: x = -6 or x = -2

x² + 6 x + 2 x + 12 = 0 ⋙ 𝐆𝐢𝐯𝐞𝐧 x² + 8 x + 12 = 0 ⋙ 𝐂𝐨𝐦𝐛𝐢𝐧𝐢𝐧𝐠 𝐥𝐢𝐤𝐞 𝐭𝐞𝐫𝐦𝐬 ( x + 6)( x + 2) = 0 ⋙ 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐯𝐞 𝐏𝐨𝐬𝐭𝐮𝐥𝐚𝐭𝐞 x + 6 = 0 or x + 2 = 0 ⋙ 𝐙𝐞𝐫𝐨 𝐩𝐫𝐨𝐝𝐮𝐜𝐭 𝐩𝐨𝐬𝐭𝐮𝐥𝐚𝐭𝐞 x = -6 or x = -2 ⋙ 𝐒𝐮𝐛𝐭𝐫𝐚𝐜𝐭𝐢𝐨𝐧 𝐩𝐫𝐨𝐩𝐞𝐫𝐭𝐲 𝐨𝐟 𝐞𝐪𝐮𝐚𝐥𝐢𝐭𝐲

Match the reasons with the statement. Given: 12 - x = 20 - 5x To Prove: x = 2

12 - x = 20 - 5x ⋙ 𝐠𝐢𝐯𝐞𝐧 12 + 4x = 20 ⋙ 𝐀𝐝𝐝𝐢𝐭𝐢𝐨𝐧 𝐩𝐫𝐨𝐩𝐞𝐫𝐭𝐲 𝐨𝐟 𝐞𝐪𝐮𝐚𝐥𝐢𝐭𝐲 4x = 8 ⋙ 𝐒𝐮𝐛𝐭𝐫𝐚𝐜𝐭𝐢𝐨𝐧 𝐩𝐫𝐨𝐩𝐞𝐫𝐭𝐲 𝐨𝐟 𝐞𝐪𝐮𝐚𝐥𝐢𝐭𝐲 x = 2 ⋙ 𝐃𝐢𝐯𝐢𝐬𝐢𝐨𝐧 𝐩𝐫𝐨𝐩𝐞𝐫𝐭𝐲 𝐨𝐟 𝐞𝐪𝐮𝐚𝐥𝐢𝐭𝐲

Match the reasons with the statements. Given: 2 (x + 3) = 8 To Prove: x = 1

2( x + 3) = 8 ⋙ 𝐆𝐢𝐯𝐞𝐧 2x + 6 = 8 ⋙ 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐯𝐞 𝐏𝐨𝐬𝐭𝐮𝐥𝐚𝐭𝐞 2x = 2 ⋙ 𝐒𝐮𝐛𝐭𝐫𝐚𝐜𝐭𝐢𝐨𝐧 𝐩𝐫𝐨𝐩𝐞𝐫𝐭𝐲 𝐨𝐟 𝐞𝐪𝐮𝐚𝐥𝐢𝐭𝐲 x = 1 ⋙ 𝐃𝐢𝐯𝐢𝐬𝐢𝐨𝐧 𝐩𝐫𝐨𝐩𝐞𝐫𝐭𝐲 𝐨𝐟 𝐞𝐪𝐮𝐚𝐥𝐢𝐭𝐲

What type of proof is used extensively in geometry?

Two-column

Which of the following can be used as "reasons" in a two-column proof?

all of the above

When developing a plan for a geometric proof, which of the following is not important?

determine the number of steps needed

Which of the following methods are useful in solving a geometric proof? Select all that apply.

• work backwards • mark the figure to reflect the given statement(s) • look at theorems related to the figure