1. 2.1 Classifying Triangles
CHAPTER
2.1 Classifying Triangles
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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.
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Definitions
Points A, B, and E are vertices. Point A is a vertex. Point B is a vertex. Point E is a vertex.
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4. 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?
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5. 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
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6. 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
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7. 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
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8. 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
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Definitions
The perimeter P of a geometric figure is the distance around the figure.
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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
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11. 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
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12. Finding the Perimeter of a Rectangle
Find the dimensions of the rectangle formed by the edging. Width of the garden and path = = 24 Length of the garden and path = = 30 Calculate the perimeter of the rectangle.
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13. Finding the Perimeter of a Rectangle
Calculate the perimeter of the rectangle. P = 2l + 2w = 2(30) + 2(24) = = 108 We need 108 feet of edging material.
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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.
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