Geometry Proofs: Questions and Verified Answers, Exams of Nursing

A series of questions and answers related to geometric proofs, focusing on two-column proofs and the properties of equality. It covers topics such as identifying the type of proof used in geometry, matching reasons with statements in algebraic proofs, and understanding the essential parts of a two-column proof. The material is designed to help students understand the logic and structure behind geometric proofs, offering practical examples and key concepts for effective problem-solving. It also includes questions about developing a plan for a geometric proof and useful methods for solving proofs, making it a valuable resource for students studying geometry.

Typology: Exams

2024/2025

Available from 08/31/2025

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PROOF FORMATS THE PLAN OF THE
PROOF QUESTIONS WITH VERIFIED
ANSWERS
What type of proof is used extensively in geometry? - ANSWERSTwo-column
Match the reasons with the statement.
Given: 12 - x = 20 - 5x
To Prove: x = 2 - ANSWERS12 - x = 20 - 5x โ‹™ ๐ ๐ข๐ฏ๐ž๐ง
12 + 4x = 20 โ‹™ ๐€๐๐๐ข๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ
4x = 8 โ‹™ ๐’๐ฎ๐›๐ญ๐ซ๐š๐œ๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ
x = 2 โ‹™ ๐ƒ๐ข๐ฏ๐ข๐ฌ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ
Match the reasons with the statements.
Given: 2 (x + 3) = 8
To Prove: x = 1 - ANSWERS2( x + 3) = 8 โ‹™ ๐†๐ข๐ฏ๐ž๐ง
2x + 6 = 8 โ‹™ ๐ƒ๐ข๐ฌ๐ญ๐ซ๐ข๐›๐ฎ๐ญ๐ข๐ฏ๐ž ๐๐จ๐ฌ๐ญ๐ฎ๐ฅ๐š๐ญ๐ž
2x = 2 โ‹™ ๐’๐ฎ๐›๐ญ๐ซ๐š๐œ๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ
x = 1 โ‹™ ๐ƒ๐ข๐ฏ๐ข๐ฌ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ
Match the reasons with the statements.
GIVEN: xยฒ + 6x + 2x + 12 = 0
TO PROVE: x = -6 or x = -2 - ANSWERSxยฒ + 6 x + 2 x + 12 = 0 โ‹™ ๐†๐ข๐ฏ๐ž๐ง
xยฒ + 8 x + 12 = 0 โ‹™ ๐‚๐จ๐ฆ๐›๐ข๐ง๐ข๐ง๐  ๐ฅ๐ข๐ค๐ž ๐ญ๐ž๐ซ๐ฆ๐ฌ
( x + 6)( x + 2) = 0 โ‹™ ๐ƒ๐ข๐ฌ๐ญ๐ซ๐ข๐›๐ฎ๐ญ๐ข๐ฏ๐ž ๐๐จ๐ฌ๐ญ๐ฎ๐ฅ๐š๐ญ๐ž
x + 6 = 0 or x + 2 = 0 โ‹™ ๐™๐ž๐ซ๐จ ๐ฉ๐ซ๐จ๐๐ฎ๐œ๐ญ ๐ฉ๐จ๐ฌ๐ญ๐ฎ๐ฅ๐š๐ญ๐ž
x = -6 or x = -2 โ‹™ ๐’๐ฎ๐›๐ญ๐ซ๐š๐œ๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ
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PROOF FORMATS THE PLAN OF THE

PROOF QUESTIONS WITH VERIFIED

ANSWERS

What type of proof is used extensively in geometry? - ANSWERSTwo-column Match the reasons with the statement. Given: 12 - x = 20 - 5x To Prove: x = 2 - ANSWERS12 - x = 20 - 5x โ‹™ ๐ ๐ข๐ฏ๐ž๐ง 12 + 4x = 20 โ‹™ ๐€๐๐๐ข๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ 4x = 8 โ‹™ ๐’๐ฎ๐›๐ญ๐ซ๐š๐œ๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ x = 2 โ‹™ ๐ƒ๐ข๐ฏ๐ข๐ฌ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ Match the reasons with the statements. Given: 2 (x + 3) = 8 To Prove: x = 1 - ANSWERS2( x + 3) = 8 โ‹™ ๐†๐ข๐ฏ๐ž๐ง 2x + 6 = 8 โ‹™ ๐ƒ๐ข๐ฌ๐ญ๐ซ๐ข๐›๐ฎ๐ญ๐ข๐ฏ๐ž ๐๐จ๐ฌ๐ญ๐ฎ๐ฅ๐š๐ญ๐ž 2x = 2 โ‹™ ๐’๐ฎ๐›๐ญ๐ซ๐š๐œ๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ x = 1 โ‹™ ๐ƒ๐ข๐ฏ๐ข๐ฌ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ Match the reasons with the statements. GIVEN: xยฒ + 6x + 2x + 12 = 0 TO PROVE: x = -6 or x = -2 - ANSWERSxยฒ + 6 x + 2 x + 12 = 0 โ‹™ ๐†๐ข๐ฏ๐ž๐ง xยฒ + 8 x + 12 = 0 โ‹™ ๐‚๐จ๐ฆ๐›๐ข๐ง๐ข๐ง๐  ๐ฅ๐ข๐ค๐ž ๐ญ๐ž๐ซ๐ฆ๐ฌ ( x + 6)( x + 2) = 0 โ‹™ ๐ƒ๐ข๐ฌ๐ญ๐ซ๐ข๐›๐ฎ๐ญ๐ข๐ฏ๐ž ๐๐จ๐ฌ๐ญ๐ฎ๐ฅ๐š๐ญ๐ž x + 6 = 0 or x + 2 = 0 โ‹™ ๐™๐ž๐ซ๐จ ๐ฉ๐ซ๐จ๐๐ฎ๐œ๐ญ ๐ฉ๐จ๐ฌ๐ญ๐ฎ๐ฅ๐š๐ญ๐ž x = -6 or x = -2 โ‹™ ๐’๐ฎ๐›๐ญ๐ซ๐š๐œ๐ญ๐ข๐จ๐ง ๐ฉ๐ซ๐จ๐ฉ๐ž๐ซ๐ญ๐ฒ ๐จ๐Ÿ ๐ž๐ช๐ฎ๐š๐ฅ๐ข๐ญ๐ฒ

When developing a plan for a geometric proof, which of the following is not important? - ANSWERSdetermine the number of steps needed Which of the following methods are useful in solving a geometric proof? Select all that apply. - ANSWERSโ€ข work backwards

  • mark the figure to reflect the given statement(s)
  • look at theorems related to the figure Which of the following can be used as "reasons" in a two-column proof? - ANSWERSall of the above In the six essential parts of a two-column proof, the proof comes after the - ANSWERSPlan of the Proof