Question

Use the info to determine if the conjecture is true or false. If a conjecture is false, give a counter example (words or pictures).

Given: ∠1 is complementary to ∠2, and ∠1 is complementary to ∠3.
Conjecture: ∠2 ≅ ∠3
a) True
b) False

Answer 1

Given that angle 1 is complementary to both angle 2 and angle 3, the conjecture that angle 2 is congruent to angle 3 is true.

Step-by-step explanation:

We are given that ∠1 is complementary to ∠2, and ∠1 is complementary to ∠3. This means that the sum of the measures of ∠1 and ∠2 is 90 degrees, and the sum of the measures of ∠1 and ∠3 is also 90 degrees. By the definition of complementary angles, if two angles sum up to 90 degrees, they are complementary. Therefore, if ∠1 + ∠2 = 90° and ∠1 + ∠3 = 90°, it must also be true that ∠2 and ∠3 are equal in measure because they both would be equal to 90° minus the measure of ∠1. So, the conjecture that ∠2 ≅ ∠3 is true.