2.1 Classifying Triangles

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Presentation transcript:

2.1 Classifying Triangles CHAPTER 2.1 Classifying Triangles Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Definitions A triangle is formed by 3 noncollinear points connected by segments. The noncollinear points are called vertices (singular is vertex). The segments joining the points are called sides. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Definitions Points A, B, and E are vertices. Point A is a vertex. Point B is a vertex. Point E is a vertex. Copyright © 2014 Pearson Education, Inc.

Identifying Parts of a Triangle Given ΔPQR: a. Which angle is opposite segment PQ? b. Which side is opposite angle Q? c. Which side is included between angle P and angle R? d. Which angle is included between segments QR and PR? Copyright © 2014 Pearson Education, Inc.

Classifying Triangles by Angles and Sides. Type Description Example Acute All (3) acute angles Obtuse 1 obtuse angle Equiangular All angles are equal. Right 1 right angle Copyright © 2014 Pearson Education, Inc.

Classifying Triangles by Angles and Sides. Type Description Example Scalene No sides are equal Isosceles At least 2 sides are equal Equilateral All sides are equal Copyright © 2014 Pearson Education, Inc.

Classifying Triangles Classify each triangle by its angles and sides. Use the most specific name. a. Angles Sides Complete Name Right Scalene Right scalene triangle Copyright © 2014 Pearson Education, Inc.

Classifying Triangles Classify each triangle by its angles and sides. Use the most specific name. b. Angles Sides Complete Name Acute Isosceles Acute isosceles triangle Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Definitions The perimeter P of a geometric figure is the distance around the figure. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Perimeter Rectangle Triangle length l and width w side lengths a, b, and c, P = 2l + 2w or 2(l + w) base b, and height h P = a + b + c Copyright © 2014 Pearson Education, Inc.

Finding the Perimeter of a Rectangle The botany club members are designing a rectangular garden for the courtyard of your school as shown to the right. They plan to place edging on the outside of the path. How much edging material will they need? Solution The red line about the outside of the path is where edging is to be placed Copyright © 2014 Pearson Education, Inc.

Finding the Perimeter of a Rectangle Find the dimensions of the rectangle formed by the edging. Width of the garden and path = 4 + 16 + 4 = 24 Length of the garden and path = 4 + 22 + 4 = 30 Calculate the perimeter of the rectangle. Copyright © 2014 Pearson Education, Inc.

Finding the Perimeter of a Rectangle Calculate the perimeter of the rectangle. P = 2l + 2w = 2(30) + 2(24) = 60 + 48 = 108 We need 108 feet of edging material. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Definitions We call the 3 original angles of a triangle the interior angles of the triangle. The angles that are adjacent to the interior angles are the exterior angles of the triangle. There are two exterior angles associated with each interior angle, but since these two exterior angles are congruent vertical angles, we usually show only one exterior angle with each interior angle. Copyright © 2014 Pearson Education, Inc.