Given: Angle A and Angle C are complementary to Angle B.
Conclusion: Angle is congruent to Angle C.
Determine whether each conclusion is valid based on the true conditional given. If not, write invalid. Explain your reasoning.
if both parents have red hair,they their children have red hair
Yes
To determine the validity of the conclusion, let's start by analyzing the given information: Angle A and Angle C are complementary to Angle B.
If two angles are complementary, it means that they add up to 90 degrees. So, we can express this relationship mathematically as:
Angle A + Angle B = 90° (Complementary angles)
Angle C + Angle B = 90° (Complementary angles)
To find if Angle A is congruent to Angle C, we need to equate these two expressions:
Angle A + Angle B = Angle C + Angle B
By canceling out the common term "Angle B" from both sides, we get:
Angle A = Angle C
So, based on the given information and the algebraic manipulation above, we can conclude that Angle A is indeed congruent to Angle C. Therefore, the conclusion is valid.