Question

in exercises 15 - 22, write the conditional statement p→q, the converse q→p, the inverse ~p→~q, and the contrapositive ~q→~p in words. then decide whether each statement is true or false. (see example 3.)

1. let p be “two angles are supplementary” and let q be “the measures of the angles sum to 180°.”
2. let p be “you are in math class” and let q be “you are in geometry.”
3. let p be “you lift weights” and let q be “you exercise.”
4. let p be “you are not an only child” and let q be “you have a sibling.”
5. let p be “an instrument is a cuatro” and let q be “the instrument is a guitar.”
6. let p be “the sun is out” and let q be “it is daytime.”
7. let p be “3x - 7 = 20” and let q be “x = 9.”
8. let p be “it is pascua florida day” and let q be “it is april.”

in exercises 23 - 26, decide whether the statement about the diagram is true. explain your answer using the definitions you have learned. (see example 4.)

1. m∠abc = 90°
2. ∠s≅∠t
3. m∠2 + m∠3 = 180°
4. m is the midpoint of ab.

Explanation:

15.

Step1: Write conditional

If two angles are supplementary, then the measures of the angles sum to 180°. (True)

Step2: Write converse

If the measures of the angles sum to 180°, then two angles are supplementary. (True)

Step3: Write inverse

If two angles are not supplementary, then the measures of the angles do not sum to 180°. (True)

Step4: Write contra - positive

If the measures of the angles do not sum to 180°, then two angles are not supplementary. (True)

Step1: Write conditional

If you are in math class, then you are in Geometry. (False)

Step2: Write converse

If you are in Geometry, then you are in math class. (True)

Step3: Write inverse

If you are not in math class, then you are not in Geometry. (True)

Step4: Write contra - positive

If you are not in Geometry, then you are not in math class. (False)

Step1: Write conditional

If you lift weights, then you exercise. (True)

Step2: Write converse

If you exercise, then you lift weights. (False)

Step3: Write inverse

If you do not lift weights, then you do not exercise. (False)

Step4: Write contra - positive

If you do not exercise, then you do not lift weights. (True)

Answer:

Conditional: True; Converse: True; Inverse: True; Contra - positive: True

16.