Altitudes and Orthocenter

What is the point of concurrency where the three altitudes of a triangle intersect?

• Incenter

• Centroid

• Orthocenter

• Circumcenter

Tags

CCSS.HSG.C.A.3

In a triangle, how many altitudes can be drawn from each vertex?

• 2

• 3

• 4

• 1

Tags

CCSS.HSG.CO.C.10

If an altitude is drawn from the vertex to the opposite side of an equilateral triangle, what type of triangle is formed?

• Right triangle

• Scalene triangle

• Isosceles triangle

• Obtuse triangle

Tags

CCSS.HSG.CO.C.10

What is the relationship between the orthocenter and the altitudes of a triangle?

• The orthocenter is the midpoint of the altitudes of a triangle.

• The orthocenter is the intersection point of the medians of a triangle.

• The orthocenter is the point where the three medians of a triangle intersect.

• The orthocenter is the point where the three altitudes of a triangle intersect.

Tags

CCSS.HSG.CO.C.10

In a right triangle, where is the orthocenter located?

• At the center of the circumscribed circle

• At the vertex adjacent to the right angle

• At the vertex opposite the right angle

• At the midpoint of the hypotenuse

Tags

CCSS.HSG.C.A.3

If the orthocenter of a triangle lies inside the triangle, what type of triangle is it?

• Obtuse triangle

• Right triangle

• Acute triangle

• Equilateral triangle

Tags

CCSS.HSG.CO.C.10

What is the orthocenter of an obtuse triangle?

• Inside the triangle

• Outside the triangle

• On the side of the triangle

• At the centroid of the triangle

Tags

CCSS.HSG.C.A.3

How does the orthocenter of an acute triangle compare to the circumcenter?

• The orthocenter is inside the circumcenter.

• The orthocenter is below the circumcenter.

• The orthocenter is on the circumcenter.

• The orthocenter is outside the circumcenter.

Tags

CCSS.HSG.C.A.3

What is the significance of the orthocenter in triangle geometry?

• The orthocenter is the point where the three perpendicular bisectors of a triangle intersect.

• The orthocenter is the point where the three angle bisectors of a triangle intersect.

• The orthocenter is the point where the three altitudes of a triangle intersect.

• The orthocenter is the point where the three medians of a triangle intersect.

Tags

CCSS.HSG.CO.C.10

How does the orthocenter of a triangle change as the triangle's angles vary?

• The orthocenter remains fixed regardless of the triangle's angles

• The orthocenter of a triangle changes as the triangle's angles vary due to the altitudes intersecting at different points.

• The orthocenter moves along the circumcircle of the triangle

• The orthocenter shifts to the midpoint of the triangle's longest side

Tags

CCSS.HSG.CO.C.10