Question

1. choose the correct answer.

if there is no indication of congruent or equal segments, you are dealing with a(n)_____
orthocenter
obtuse
acute
right

1. choose the correct answer.

the orthocenter will lie at the vertex of the right angle in a(n)_____triangle.
obtuse
acute
circumcenter
right

1. choose the correct answer.

the orthocenter will lie in the interior of a(n)_____triangle.
acute
right
circumcenter

Explanation:

Question 9

When there's no indication of congruent or equal segments in a triangle, we consider the general case. An orthocenter is a point of intersection of altitudes, not a triangle type. Obtuse (has one angle >90°), acute (all angles <90°), and right (one 90° angle) are triangle types. Without congruent/equal segments, we assume a non - isoceles, non - equilateral triangle, but the key here is that the question is about the type when no equal segments are indicated. However, the correct answer here is about the triangle type related to orthocenter? Wait, no, re - reading: "If there is no indication of congruent or equal segments, you are dealing with a(n) __". Wait, maybe a mis - phrasing, but the options: orthocenter is a point, not a triangle. Obtuse, acute, right are triangle types. But maybe the question is about the triangle where orthocenter... No, the options: orthocenter is a point, so the other options are triangle types. Wait, maybe the question is wrong, but among the options, "orthocenter" is a point, not a triangle. Wait, no, maybe the question is "If there is no indication of congruent or equal segments, you are dealing with a(n) triangle" (missing "triangle"). Then, without equal segments, it's a scalene triangle, but the options don't have scalene. Wait, the options are orthocenter, obtuse, acute, right. So maybe the question is about the orthocenter's location? No, the first question: "If there is no indication of congruent or equal segments, you are dealing with a(n) ". Maybe a mistake, but among the options, "orthocenter" is a point, not a triangle. Wait, maybe the question is "If there is no indication of congruent or equal segments, the triangle is " (scalene), but since scalene is not an option, maybe the question is misprinted. But looking at the options, maybe the intended answer is "orthocenter" is wrong, maybe the question is about triangle type when no equal sides: scalene, but not in options. Alternatively, maybe the question is "If there is no indication of congruent or equal segments, you are dealing with a(n) __ (triangle type where orthocenter... No, this is confusing. Wait, maybe the first question is a mistake, but let's check the second question.

Question 10

In a right triangle, the altitudes corresponding to the legs are the legs themselves, and the altitude to the hypotenuse is inside the triangle. The orthocenter (intersection of altitudes) in a right triangle lies at the vertex of the right angle because the two legs are altitudes, and their intersection is the right - angled vertex. In an obtuse triangle, the orthocenter is outside; in an acute triangle, it's inside. "Circumcenter" is a different center (intersection of perpendicular bisectors). So the correct answer is right.

In an acute triangle (all angles less than 90°), the orthocenter (intersection of altitudes) lies inside the triangle. In a right triangle, it lies at the right - angled vertex. In an obtuse triangle, it lies outside. "Circumcenter" is not a triangle type. So the correct answer is acute.

Answer:

D. right (assuming the options are labeled A: obtuse, B: acute, C: circumcenter, D: right)

Question 11