logical reasoning complete the statement using always, sometimes, or never.
22. an isosceles triangle is __?__ an equilateral triangle.
23. an obtuse triangle is __?__ an isosceles triangle.
24. an interior angle of a triangle and one of its adjacent exterior angles are __?__ supplementary.
25. the acute angles of a right triangle are __?__ complementary.
26. a triangle __?__ has a right angle and an obtuse angle.

Question

Accepted Answer

# Explanation:
## 22. An isosceles triangle is sometimes an equilateral triangle.
An isosceles triangle has at least two equal sides. An equilateral triangle has all three sides equal. So, when an isosceles triangle has all three sides equal (which is a special case), it is an equilateral triangle. But not all isosceles triangles have three equal sides.
## 23. An obtuse triangle is sometimes an isosceles triangle.
An obtuse triangle has one angle greater than $90^{\circ}$. An isosceles triangle has at least two equal sides (and equal angles). There are obtuse - isosceles triangles (e.g., angles $120^{\circ},30^{\circ},30^{\circ}$) but also obtuse non - isosceles triangles (e.g., angles $100^{\circ},50^{\circ},30^{\circ}$).
## 24. An interior angle of a triangle and one of its adjacent exterior angles are always supplementary.
By the definition of adjacent angles and the linear - pair postulate, if $\angle A$ is an interior angle of a triangle and $\angle B$ is its adjacent exterior angle, then $\angle A+\angle B = 180^{\circ}$ (since they form a linear pair).
## 25. The acute angles of a right triangle are always complementary.
In a right triangle, if one angle is $90^{\circ}$, and the sum of the interior angles of a triangle is $180^{\circ}$. Let the two acute angles be $x$ and $y$. Then $x + y+90^{\circ}=180^{\circ}$, so $x + y=90^{\circ}$.
## 26. A triangle never has a right angle and an obtuse angle.
The sum of the interior angles of a triangle is $180^{\circ}$. A right angle is $90^{\circ}$ and an obtuse angle is greater than $90^{\circ}$. If we have a right angle ($90^{\circ}$) and an obtuse angle ($>90^{\circ}$), their sum is $>180^{\circ}$, which violates the triangle - angle - sum theorem ($\angle1+\angle2+\angle3 = 180^{\circ}$ for a triangle with angles $\angle1,\angle2,\angle3$).

# Answer:
22. sometimes
23. sometimes
24. always
25. always
26. never

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Question

Explanation:

22. An isosceles triangle is sometimes an equilateral triangle.

23. An obtuse triangle is sometimes an isosceles triangle.

24. An interior angle of a triangle and one of its adjacent exterior angles are always supplementary.

25. The acute angles of a right triangle are always complementary.

26. A triangle never has a right angle and an obtuse angle.

Answer: