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

2. 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.

3. 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

4. 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.

5. Acute Triangle
All 3 angles are acute angles

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

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

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

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

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

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

12. Find the Missing Angle

13. Find the Missing Angle

14. 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.

15. End of day 1…Day 2…

16. 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

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

18. 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

19. 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

20. 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

21. 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.