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We are given the following diagram.
We want to determine which of the given statements is not true concerning ∠A, ∠B, and ∠C. Let's analyze the statements one at a time.
First, we will consider statement F.
∠B and ∠C are obtuse angles. |
Recall that obtuse angles are angles that measure more than 90∘ but less than 180∘. Let's look at ∠B and ∠C.
We can see that ∠B and ∠C are right angles. Since these angles have a measure of 90∘, they are not obtuse. Therefore, statement F is not true.
Now we will analyze statement G.
∠A and ∠C are vertical angles. |
When two lines or line segments intersect, vertical angles are formed on opposite sides of the point of intersection. To check whether ∠A and ∠C are vertical, let's take another look at the diagram.
Notice that ∠A and ∠C are on opposite sides of the point of intersection of two lines. This means that these angles are vertical, so statement G is true.
Next, we will consider statement H.
∠A and ∠B are alternate interior angles. |
Notice that in the diagram, we have two parallel lines that are cut by a transversal. Recall that alternate interior angles are interior angles that lie on opposite sides of the transversal. Looking at the diagram, we can determine whether ∠A and ∠B are alternate interior angles.
Indeed, ∠A and ∠B are interior angles that lie on opposite sides of the transversal. Therefore, these angles are alternate interior angles, and statement H is true.
Finally, we will analyze statement I.
∠A and ∠C are congruent. |
Since statement G is true, we know that ∠A and ∠C are vertical angles. Recall that vertical angles are always congruent. This means that ∠A and ∠C are congruent and statement I is also true.
We found that only statement F is not true.