7.G.5 Triangles and 7.G.5 Triangles and AnglesAngles

7.G.5 Triangles and 7.G.5 Triangles and AnglesAngles

GeometryGeometryMr. NealeyMr. Nealey77thth Grade Grade

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Standard/Objectives:Objectives:• Classify triangles by their sides and

angles.• Find missing angle measures in

trianglesDEFINITION: A triangle is a figure formed

by three line segments joining three non-collinear points.

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Names of triangles

Equilateral—3 congruent sides

Isosceles Triangle—2 congruent sides

Scalene—no congruent sides

Triangles can be classified by the congruency of their sides.

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Triangles by Angles• Triangles can also be classified by

the size of their largest angle. All triangles have at least 2 acute angles, the smallest of the 3.

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Acute Triangle

mCAB = 41.76 mBCA = 67.97

mABC = 70.26

B

A

C

All 3 angles are acute angles

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Right Triangle• Has only 1 right

angle• Has only 1 obtuse

angle

Obtuse Triangle

Sum of the Angles• Label your

triangle with angles A, B, and C.

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Sum of the Angles• Tear the angles

off your triangle, being careful to preserve the corners.

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Sum of the Angles• Connect the tips

of your triangle together.

• When you add all 3 angles, what does the sum appear to be?

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Sum of the Angles• What is the sum

of the interior angles of any triangle?

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Finding the missing Angle

• What is the sum of the interior angles of any triangle?

• 180 Degrees

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Find the Missing Angle

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Find the Missing Angle

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Triangles• Use P.430 in the Course 2 Book #3-23• Find missing angles using 180 degrees• Identify the Triangles by their sides and

angles.

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End of day 1…Day 2…

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Parts of a 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

B

C

A

adjacent

adjacent

Side opposite A

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Right Triangle• Red represents

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

hypotenuseleg

leg

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• 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 the base.

leg

leg

base

Isosceles Triangles

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Identifying the parts of an isosceles triangle

• 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.

A B

C

About 7 ft.

5 ft 5 ft

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Identifying the parts of an isosceles triangle

• 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.

A B

C

About 7 ft.

5 ft 5 ftleg leg

Hypotenuse & Base

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A

B

C

Using Angle Measures of Triangles 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.