Define altitudes, construct them using a set square, and classify triangles by angles.
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Visual of altitudes inside and outside triangles.
An altitude is always drawn perpendicular to the base line, even if it falls entirely outside the triangle's physical boundaries.
Define altitude as the perpendicular from a vertex to the opposite side.
In the world around us, we often talk about heights—of people, trees, or buildings. But what does the "height" of a triangle mean? We measure it by drawing a line segment straight down from a top vertex to the base.
Step-by-step use of a set square.
Given an arbitrary triangle ABC resting on base BC, construct the altitude from vertex A to base BC using simple drafting tools to guarantee a precise angle.
Define acute-angled, right-angled, and obtuse-angled triangles.
Just as we classify triangles by their side lengths (equilateral, isosceles, scalene), we can also categorize them by their internal angle measures. The classification depends on the largest angle within the triangle.
Question identifying which triangle has sides serving as altitudes.
In which type of triangle is one of its sides also an altitude?
Determine possible angle combinations for specific triangle types.
Imagine you construct a right-angled triangle with . What combined values can and take? Follow the steps below to deduce this algebraically.
State the known angle.
State the Angle Sum Property equation for triangle ABC.
Substitute the known value of angle B into the formula.
Show the algebraic step to isolate angle A and angle C.
What is the combined sum of angle A and angle C?
Since their sum is 90 degrees and both must be positive, what type of angles are A and C?