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4.1 Triangles and AnglesPowerPoint Presentation

4.1 Triangles and Angles

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4.1 Triangles and Angles

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4.1 Triangles and Angles

Geometry

Mrs. Spitz

Fall 2004

Standard 3: Students will learn and apply geometric concepts.

Objectives:

- Classify triangles by their sides and angles.
- Find angle measures in triangles
DEFINITION: A triangle is a figure formed by three segments joining three non-collinear points.

- 4.1 Worksheet A and B
- Chapter 4 Definitions – pg. 192
- Chapter 4 Postulates/Theorems – green boxes within chapter 4
- Binder check Monday/Tuesday

Triangles can be classified by the sides or by the angle

Equilateral—3 congruent sides

Isosceles Triangle—2 congruent sides

Scalene—no congruent sides

3 acute angles

- 3 congruent angles. An equiangular triangle is also acute.

1 right angle

Obtuse Triangle

Each of the three points joining the sides of a triangle is a vertex.(plural: vertices). A, B and C are vertices.

Two sides sharing a common vertext are adjacent sides.

The third is the side opposite an angle

adjacent

Side opposite A

adjacent

Red represents the hypotenuse of a right triangle. The sides that form the right angle are the legs.

hypotenuse

leg

leg

An isosceles triangle can have 3 congruent sides in which case it is equilateral. When an isosceles triangle has only two congruent sides, then these two sides are the legs of the isosceles triangle. The third is thebase.

Isosceles Triangles

leg

base

leg

Explain why ∆ABC is an isosceles right triangle.

In the diagram you are given that C is a right angle. By definition, then ∆ABC is a right triangle. Because AC = 5 ft and BC = 5 ft; AC BC. By definition, ∆ABC is also an isosceles triangle.

About 7 ft.

5 ft

5 ft

Identify the legs and the hypotenuse of ∆ABC. Which side is the base of the triangle?

Sides AC and BC are adjacent to the right angle, so they are the legs. Side AB is opposite the right angle, so it is t he hypotenuse. Because AC BC, side AB is also the base.

Hypotenuse & Base

About 7 ft.

5 ft

5 ft

leg

leg

Smiley faces are interior angles and hearts represent the exterior angles

Each vertex has a pair of congruent exterior angles; however it is common to show only one exterior angle at each vertex.

Exterior Angle theorem: m1 = m A +m 1

x + 65 = (2x + 10)

65 = x +10

55 = x

65

(2x+10)

x

Corollary to the triangle sum theorem

The acute angles of a right triangle are complementary.

m A + m B = 90

2x

x

X + 2x = 90

3x = 90

X = 30

So m A = 30 and the m B=60

B

2x

x

A

C