module 5 lesson 2 4
TRANSCRIPT
Module 5 Lesson 24 Area of All Triangles Combined.notebook
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Answers Problem Set Lesson 1
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MODULE 5 Area, Surface Area, and Volume Problems
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 2: The Area of Right TrianglesStudent Outcomes§ Students jusfy the area formula for a right triangle by viewing the right triangle as part of a rectangle composed of two right triangles.
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a = bh4cm
9cm
a = 4cm
9cm
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MODULE 5 Area, Surface Area, and Volume Problems
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 3: The Area of All TrianglesStudent Outcomes§ Students show the area formula for a triangular region by decomposing a triangle into right triangles. For a given triangle, the height of the triangle is the length of the altude. The length of the base is either called the length base or, more commonly, the base.
§ Students understand that the height of the triangle is the perpendicular segment from a vertex of a triangle to the line containing the opposite side. The opposite side is called the base. Students understand that any side of a triangle can be considered a base and that the choice of base determines the height.
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Remember in Lesson 1......How do we find the area of a rectangle?
How do we find the area of a parallelogram?
We needed to find the HEIGHT by making a right angle with the base...
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4cm
3cm 3cm
6cm
8cm
10cm3cm
4cm
It was easy to find the area of a right triangle because the side was the height.
But what about these??
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Notice that by drawing the altitude we have created two right triangles. How can we calculate the area of the entire triangle?
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MODULE 5 Area, Surface Area, and Volume Problems
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 4: The Area of All TrianglesStudent Outcomes§ Students construct the altude for three different cases: an altude that is a side of a right angle, an altude that lies over the base, and an altude that is outside the triangle.
§ Students deconstruct triangles to jusfy that the area of a triangle is exactly one half the area of a parallelogram.
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Closing
Please take out your exit ticket for Lesson 2,3,4, close your binder, and complete the exit ticket. This will be collected.
§ How are the area formulas of rectangles and right triangles related?ú Every type of triangle fits inside exactly half of a rectangle that has the same base and height lengths.
§ When a triangle is not a right triangle, how can you determine its base and height?ú The height of a triangle is the length of the altude. The altude is the line segment from a vertex of a triangle to the line containing the opposite side (or the base) that is perpendicular to the base.
§ Why does the area formula for a triangle work for every triangle?ú Every type of triangle fits inside exactly half of a rectangle that has the same base and height lengths.