Understanding Altitudes and Orthocenters in Triangles

This video tutorial explains the concept of altitudes in triangles, focusing on acute, right, and obtuse triangles. It describes how altitudes are line segments from a vertex perpendicular to the opposite side, and introduces the orthocenter, the intersection point of altitudes. The orthocenter's location varies: inside for acute triangles, at the right angle for right triangles, and outside for obtuse triangles.

What is the altitude of a triangle?

• A line segment parallel to one side of a triangle

• A line segment bisecting an angle of a triangle

• A line segment from a vertex to the opposite side, perpendicular to it

• A line segment connecting two sides of a triangle

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CCSS.HSG.C.A.3

In an acute triangle, where is the orthocenter located?

• Outside the triangle

• On the hypotenuse

• Inside the triangle

• At the midpoint of a side

How many altitudes can be drawn in a triangle?

• One

• Four

• Two

• Three

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In a right triangle, where is the orthocenter found?

• At the right angle vertex

• Inside the triangle

• Outside the triangle

• At the midpoint of the hypotenuse

Which side is opposite to vertex A in triangle ABC?

• Side AB

• Side CA

• Side AC

• Side BC

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CCSS.HSG.C.A.3

In an obtuse triangle, where is the orthocenter located?

• At the obtuse angle vertex

• Inside the triangle

• On the longest side

• Outside the triangle

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CCSS.HSG.C.A.3

What must be done to find the orthocenter in an obtuse triangle?

• Extend the sides of the triangle

• Find the centroid first

• Draw medians instead of altitudes

• Use only the acute angles

What is the first step in drawing an altitude from vertex A?

• Draw a line parallel to side AB

• Draw a line parallel to side BC

• Draw a line perpendicular to side BC

• Draw a line bisecting angle A

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What is the orthocenter?

• The point where all medians intersect

• The point where all perpendicular bisectors intersect

• The point where all altitudes intersect

• The point where all angle bisectors intersect

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What is the purpose of the practical exercise in the video?

• To find the centroid of a triangle

• To measure angles in a triangle

• To draw altitudes and find the orthocenter

• To calculate the area of a triangle

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CCSS.HSG.C.A.3