Constructing Altitudes in Triangles

This video tutorial explains how to construct the altitude of a triangle, which is a line segment from a vertex perpendicular to the opposite side. It covers the concept of altitudes and the orthocenter, the point where all three altitudes intersect. The tutorial provides step-by-step instructions for constructing altitudes in both acute and obtuse triangles using a compass and straightedge.

What is the point of concurrency of the altitudes in a triangle called?

• Orthocenter

• Incenter

• Circumcenter

• Centroid

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CCSS.HSG.CO.C.10

How many altitudes does a triangle have?

• Four

• One

• Three

• Two

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CCSS.HSG.CO.C.10

What tool is necessary to construct an altitude in a triangle?

• Calculator

• Compass

• Ruler

• Protractor

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CCSS.HSG.CO.C.10

When constructing an altitude in an acute triangle, what is the first step?

• Place the compass on the vertex

• Draw a perpendicular line

• Measure the angle

• Extend the opposite side

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CCSS.HSG.CO.C.9

In constructing an altitude for an acute triangle, why do you swing arcs above and below the side?

• To measure the angle

• To ensure arcs intersect

• To create a perpendicular bisector

• To find the midpoint

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CCSS.HSG.CO.C.10

What is a key difference when constructing an altitude in an obtuse triangle compared to an acute triangle?

• Extend the opposite side

• Use a different vertex

• Measure the angle first

• Use a different tool

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CCSS.HSG.CO.C.10

Why is it necessary to extend the opposite side when constructing an altitude in an obtuse triangle?

• To make the triangle larger

• To find the midpoint

• To create a perpendicular segment

• To measure the angle

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CCSS.HSG.CO.C.9

What should you do after swinging arcs from the points of intersection in an obtuse triangle?

• Extend the opposite side further

• Measure the angle

• Use a protractor to check angles

• Draw a line through the vertex and arc intersections

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CCSS.HSG.CO.C.10

What ensures that the constructed line is an altitude in an obtuse triangle?

• It is perpendicular to the extended side

• It is the longest side

• It bisects the angle

• It is parallel to the opposite side

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CCSS.HSG.CO.C.10

What is the final step in constructing an altitude in any triangle?

• Extend the altitude beyond the triangle

• Measure the length of the altitude

• Check the angle with a protractor

• Align the straightedge with the vertex and arc intersections