Geometry Mr. Nealey 7th Grade 7.G.5 Triangles and Angles Geometry Mr. Nealey 7th Grade

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

Names of triangles Triangles can be classified by the congruency of their sides. Equilateral—3 congruent sides Isosceles Triangle—2 congruent sides Scalene—no congruent sides

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.

Acute Triangle All 3 angles are acute angles

Right Triangle Obtuse Triangle Has only 1 right angle Has only 1 obtuse angle

Sum of the Angles Label your triangle with angles A, B, and C.

Sum of the Angles Tear the angles off your triangle, being careful to preserve the corners.

Sum of the Angles Connect the tips of your triangle together. When you add all 3 angles, what does the sum appear to be?

Sum of the Angles What is the sum of the interior angles of any triangle?

Finding the missing Angle What is the sum of the interior angles of any triangle? 180 Degrees

Find the Missing Angle

Find the Missing Angle

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.

End of day 1…Day 2…

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 adjacent Side opposite A adjacent

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

Isosceles Triangles 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 base leg

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. About 7 ft. 5 ft 5 ft

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. Hypotenuse & Base About 7 ft. 5 ft 5 ft leg leg

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.