Question

1. choose the correct answer.

the orthocenter will lie in the exterior of a(n)_____triangle
circumcenter
acute
obtuse
nght

1. choose the correct answer.

which triangle involves perpendicular bisectors?
d
b
c
a

Explanation:

Question 12

The orthocenter is the intersection of a triangle's altitudes. In an acute triangle, all altitudes are inside, so the orthocenter is inside. In a right triangle, the orthocenter is at the right - angled vertex. In an obtuse triangle, one altitude is outside the triangle, so the orthocenter (intersection of altitudes) lies outside the triangle. "Circumcenter" is not a type of triangle.

Perpendicular bisectors of a triangle are lines that are perpendicular to a side and bisect it (divide it into two equal parts). Let's analyze each option:

• Option A: The markings show that \(AX=\frac{1}{2}AC\), \(BY = \frac{1}{2}BA\), \(CZ=\frac{1}{2}CB\) and the lines are perpendicular to the sides (since they bisect and are perpendicular, as indicated by the right - angle - like markings and the mid - point markings). So these are perpendicular bisectors.
• Option B: The markings \(AP = YP=ZP\) suggest it is related to angle bisectors or in - center (in - center is equidistant from sides), not perpendicular bisectors.
• Option C: The markings with right angles on the sides (not bisecting the sides but being altitudes maybe) do not indicate perpendicular bisectors.
• Option D: The markings \(AP = BP = CP\) suggest it is related to the circum - center (circum - center is equidistant from vertices), but the lines here are not perpendicular bisectors in the way option A is.

So the triangle with perpendicular bisectors is option A.

Answer:

C. obtuse

Question 13