Bell Work: Name this polygon. Is it regular or irregular?

Answer: Hexagon, irregular

Lesson 20: Triangles

Triangle: a polygon with three sides. We classify triangles based on their angle measures and based on the relative lengths of their sides.

Triangles are classified as acute, right, or obtuse based on the measure of their largest angle. The measure of the three angles of a triangle total 180 degrees, so at least 2 angles of a triangle are acute.

Triangles are also classified by relative side lengths.

Equilateral*: triangles have three equal-length sides. (and three equal angles)

Isosceles*: triangles have at least two equal-length sides. (and at least two equal angles)

Scalene*: triangles have sides of different lengths. (and angles of different measures)

We can use tick marks and arcs to indicate sides and angles that have equal measures. Any triangle can be classified both by angles and by sides.

Can an equilateral triangle be an obtuse triangle? Why or why not?

Answer: No, equilateral triangles have three equal sides and three equal angles that are acute.

Example: Classify triangle ABC by angles and sides. A B C 60°

Answer: The triangle is a right triangle and a scalene triangle.

Example: The roof of the building in the drawing slopes 35°. What is the measure of the angle at the peak of the roof? 35°

Answer: 35° + 35° + x = 180° X = 110°

Now we will consider how to find the area of a triangle. Triangle ABC is enclosed by a rectangle. What fraction of the area of the rectangle is the area of triangle ABC? A BC

The perpendicular dimensions of a triangle are called the base and height. Multiplying the base and height of a triangle gives us the area of a rectangle with the same base and height. Since a triangle occupies half the area of the rectangle, we find the area by finding half the area of the rectangle.

Area of a Triangle = ½ base x height = ½ bh

Example: Find the area of the triangle.

Answer: = ½ (8cm)(5cm) = ½(40cm ) = 20cm 2 2

Example: Find the area of the triangle.

Answer: = ½ (4 units)(3 units) = ½(12 units ) = 6 units 2 2

HW: Lesson 20 #1-30 Due Next Time