7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.
-
Upload
teagan-ventre -
Category
Documents
-
view
213 -
download
0
Transcript of 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.
![Page 1: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/1.jpg)
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
![Page 2: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/2.jpg)
2
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.
![Page 3: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/3.jpg)
3
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.
![Page 4: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/4.jpg)
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.
![Page 5: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/5.jpg)
5
Acute Triangle
mCAB = 41.76 mBCA = 67.97
mABC = 70.26
B
A
C
All 3 angles are acute angles
![Page 6: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/6.jpg)
6
Right Triangle• Has only 1 right
angle• Has only 1 obtuse
angle
Obtuse Triangle
![Page 7: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/7.jpg)
Sum of the Angles• Label your
triangle with angles A, B, and C.
7
![Page 8: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/8.jpg)
Sum of the Angles• Tear the angles
off your triangle, being careful to preserve the corners.
8
![Page 9: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/9.jpg)
Sum of the Angles• Connect the tips
of your triangle together.
• When you add all 3 angles, what does the sum appear to be?
9
![Page 10: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/10.jpg)
Sum of the Angles• What is the sum
of the interior angles of any triangle?
10
![Page 11: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/11.jpg)
Finding the missing Angle
• What is the sum of the interior angles of any triangle?
• 180 Degrees
11
![Page 12: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/12.jpg)
Find the Missing Angle
12
![Page 13: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/13.jpg)
Find the Missing Angle
13
![Page 14: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/14.jpg)
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.
14
![Page 15: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/15.jpg)
End of day 1…Day 2…
15
![Page 16: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/16.jpg)
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
B
C
A
adjacent
adjacent
Side opposite A
![Page 17: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/17.jpg)
17
Right Triangle• Red represents
the hypotenuse of a right triangle. The sides that form the right angle are the legs.
hypotenuseleg
leg
![Page 18: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/18.jpg)
18
• 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
![Page 19: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/19.jpg)
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.
A B
C
About 7 ft.
5 ft 5 ft
![Page 20: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/20.jpg)
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.
A B
C
About 7 ft.
5 ft 5 ftleg leg
Hypotenuse & Base
![Page 21: 7.G.5 Triangles and Angles Geometry Mr. Nealey 7 th Grade.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551afcd855034607418b47ba/html5/thumbnails/21.jpg)
21
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.