7.2(b) Notes: Altitudes of Triangles Date: 7.2(b) Notes: Altitudes of Triangles   Lesson Objective: Identify and use altitudes in triangles CCSS: G.CO.10, G.MG.3 You will need: colored pens, CPR This is Jeopardy!!!:  This is another name for the height of a triangle.

Lesson 1: The Altitudes and Orthocenter Altitude of a ∆: A | segment from a vertex to the opposite side; also called the height of a ∆.   Orthocenter: The point of con­cur­rency of the altitudes.

Lesson 1: The Altitudes and Orthocenter Draw scalene ∆ABC with a straightedge. B A C

Lesson 1: The Altitudes and Orthocenter With your compass, construct the altitude BG _|_ to AC. B A C

Lesson 1: The Altitudes and Orthocenter Use a protractor or ID card to draw the altitude CD and AF _|_ to AB and BC. B A C

Lesson 1: The Altitudes and Orthocenter B A C The lines containing altitudes CD, AF and BG intersect at P, the orthocenter of ΔABC.

Lesson 2: Finding the Altitudes on the Coordinate Plane Find the altitudes of ΔABC with vertices A(0, -8), B(2, -2) and C(8, -8).

Lesson 3: Finding the Altitudes on the Coordinate Plane Find the altitudes of ΔXYZ with vertices X(-6, 2), Y(-3, -2) and Z(-6, -8).

7.2(b): Do I Get It? Yes or No Use a compass to construct an Isosceles triangle with its base longer than the other 2 sides. Construct the altitude of each side. Find the altitudes of each side of the triangles with the following vertices. J(3, -2), K(5, 6) and L(9, -2) R(-7, 10), S(-1, 10) and T(-1, 1). Use a compass to construct an equilateral triangle. Construct the altitude of each side.