Can someone help me with Always, Sometimes, Never questions??

I have answered all of these, but I am not sure if they are right.

1. The base angle of an isosceles triangle are acute----Always

2. When the altitude and the median are drawn from the same vertex of a triangle, the altitude is longer than the median-----Always

3. In triangle ABC, if AB is greater than AC, then <C is greater than <B-----Always

4. All three altitudes of a triangle lie outside the triangle----Sometimes

5. If an exterior angle of a triangle is obtuse, then the triangle is acute---Sometimes

1 ok

2 never
3 ok
4 never
5 ok

Sure, I can help you with these Always, Sometimes, Never questions and explain how to determine the correct answers. Here are the explanations for each question:

1. The base angle of an isosceles triangle are acute - Always:
To determine if this statement is always true, we need to understand the characteristics of an isosceles triangle. In an isosceles triangle, two sides are congruent. Due to the triangle's symmetry, the base angles opposite these congruent sides are also congruent. Since acute angles measure less than 90 degrees, and congruent angles have the same measure, the base angles of an isosceles triangle are always acute.

2. When the altitude and the median are drawn from the same vertex of a triangle, the altitude is longer than the median - Always:
To determine the validity of this statement, we need to recall the properties of altitudes and medians in a triangle. An altitude is a line segment drawn from a vertex perpendicular to the opposite side, while a median is a line segment connecting a vertex to the midpoint of the opposite side. Now, if we draw these segments from the same vertex, the altitude will always be longer than the median. This is because the altitude is the shortest distance between the vertex and the opposite side, while the median is longer as it extends to the midpoint.

3. In triangle ABC, if AB is greater than AC, then angle C is greater than angle B - Sometimes:
To determine if this statement is sometimes true or not, we need to consider the relationship between side lengths and angle measures in a triangle. According to the Triangle Inequality Theorem, in a triangle, the sum of any two sides must be greater than the third side. If AB is greater than AC, it implies that side BC must be shorter than both AB and AC since it is the remaining side. Now, applying the Angle-Side Relationship, we find that the larger side is always opposite the larger angle. Therefore, if AB is greater than AC, angle C will be greater than angle B.

4. All three altitudes of a triangle lie outside the triangle - Sometimes:
To determine if this statement is sometimes true, we need to understand the different types of triangles. In an obtuse-angled triangle, where one angle is greater than 90 degrees, all three altitudes lie outside the triangle. However, in an acute-angled triangle, where all angles are less than 90 degrees, all three altitudes will lie inside the triangle. Therefore, the statement is sometimes true, depending on the type of triangle.

5. If an exterior angle of a triangle is obtuse, then the triangle is acute - Sometimes:
To determine if this statement is sometimes true, we need to understand the relationship between exterior angles and interior angles in a triangle. An exterior angle of a triangle is formed by extending one of its sides. The sum of the measures of an exterior angle and its corresponding interior angle is always 180 degrees. Now, if an exterior angle is obtuse (measure greater than 90 degrees), its corresponding interior angle will be acute. However, this does not imply that the entire triangle is acute. It is possible for the other two interior angles to be obtuse or a combination of obtuse and acute. Therefore, the statement is sometimes true, depending on the measures of the other interior angles in the triangle.

I hope these explanations help clarify the answers for you. If you have any further questions or need more assistance, please let me know!