Question

for exercises 24–29, draw a valid conclusion from the given statements, if possible. then state whether your conclusion was drawn using the law of detachment or the law of syllogism. if no valid conclusion can be drawn, write no valid conclusion. explain your reasoning. 24. given: if a figure is a square, then all the sides are congruent. figure abcd is a square. 25. given: if two angles are complementary angles, the sum of the measures of the angles is 90°. ∠1 and ∠2 are complementary angles. 26 given: ballet dancers like classical music. if you like classical music, then you enjoy the opera. 27. given: if you are an athlete, then you enjoy sports. if you are competitive, then you enjoy sports. 28. given: if a polygon is regular, then all of its sides are congruent. all of the sides of polygon wxyz are congruent. 29. given: if terryl completes a course with a grade of c, then he will not receive credit. if terryl does not receive credit, he will have to take the course again.

Explanation:

24

The first statement is a conditional "if - then" statement. The second statement affirms the hypothesis (the "if" part). By the Law of Detachment, we can draw a conclusion.

The first statement is a conditional about complementary angles. The second statement affirms the hypothesis. By the Law of Detachment, we can draw a conclusion.

We have two conditional statements where the conclusion of the first is the hypothesis of the second. By the Law of Syllogism, we can draw a conclusion.

Answer:

All the sides of figure \(ABCD\) are congruent. Law of Detachment.

25