Title: COMPLETE: Guided Practice
Course: Geometry (A)

Complete the questions below. The answers are listed below so you can check your answers.

Review Questions

Write the hypothesis and the conclusion for each statement.

1. If divides evenly into , then is an even number.
2. If a triangle has three congruent sides, it is an equilateral triangle.
3. All equiangular triangles are equilateral.
4. What is the converse of the statement in exercise 1 above? Is the converse true?
5. What is the inverse of the statement in exercise 2 above? Is the inverse true?
6. What is the contrapositive of the statement in exercise 3? Is the contrapositive true?
7. The converse of a statement about collinear points , , and is: If and , then is the midpoint of .
  - What is the statement?
  - Is it true?
8. What is the inverse of the inverse of if then ?
9. What is the one-word name for the converse of the inverse of an if-then statement?
10. What is the one-word name for the inverse of the converse of an if-then statement?

For each of the following biconditional statements:

- Write in words.
- Write in words.
- Is true?
- Is true?
- Is true?

Note that in these questions, and could be reversed and the answers would be correct.

1. A U.S. citizen can vote if and only if he or she is or more years old.
2. A whole number is prime if and only if it is an odd number.
3. Points are collinear if and only if there is a line that contains the points.
4. if only if and

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Review Answers

1. Hypothesis: divides evenly into ; conclusion: is an even number.
2. Hypothesis: A triangle has three congruent sides; conclusion: it is an equilateral triangle.
3. Hypothesis: A triangle is equiangular; conclusion: the triangle is equilateral.
4. If is an even number, then divides evenly into . True.
5. If a triangle does not have three congruent sides, then it is not an equilateral triangle. True.
6. If a triangle is not equilateral, then it is not equiangular. True.
7. If is the midpoint of , then and . False ( and could both be , , etc.).
8. If then
9. Contrapositive
10. Contrapositive
11. he or she is or more years old; a U. S. citizen can vote; is true; is true; is true.
12. a whole number is an odd number; a whole number is prime; is false; is false; is false.
13. a line contains the points; the points are collinear; is is true; is true; is true.
14. and ; ; is true; is false; is false.