triangles 101
TRANSCRIPT
![Page 1: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/1.jpg)
• Triangular Shape• Electromagnetism• The Lost Continent
of Atlantis• Portal to Another
Dimension
![Page 2: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/2.jpg)
TRIANGLES
![Page 3: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/3.jpg)
• A set of points is a triangle if and only if it consists of the figure formed by three segments connecting three noncollinear points.
• Each of the three noncollinear points is called a vertex.
• The segments are called the sides.
Definition
vertex
vertex vertex
side side
side
![Page 4: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/4.jpg)
NAMING A TRIANGLE AND ITS PARTS
• Triangle ABC / ΔABC
• Angles: A, B, & C
• Sides: AB, BC, & CA
a, b, & cA
B
C
c a
b
Note: Naming = Consecutive vertices (preferably clockwise)
![Page 5: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/5.jpg)
TRIANGLE CLASSIFICATION (ACCDG. TO SIDES) pg 129
SCALENENo sides congruent
ISOSCELESAt least 2 sides congruent
EQUILATERALAll sides congruent
Using the Geoboards
![Page 6: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/6.jpg)
TRIANGLE CLASSIFICATION (ACCDG. TO ANGLES) pg 129
ACUTE3 acute angles
RIGHT1 right angle
OBTUSE1 obtuse angle
EQUIANGULARAll angles congruent
┌
![Page 7: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/7.jpg)
Paper-folding Investigation
Draw a triangle similar in shape to the ΔABC. Cut it out.
• Slide point A along AC toward point C until the fold passes through point B. The crease intersects AC at point D. Unfold the triangle.
A
B
C
A
B
CD
A
B
CD
![Page 8: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/8.jpg)
• Bring point A to point D and crease.
• Bring points B and C to point D and crease.
A
B
CD
A B CD
What appears to be true about the sum of the measures of these angles three angles?
![Page 9: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/9.jpg)
The sum of the measures of angles of a triangle is 180o.
A
B
CA B C
A + B + C = 180o
1 2
34 5
pg 110 - 111
![Page 10: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/10.jpg)
Sample Problems
1. The angles of a triangle are in a ratio 3:4:5. Find the measures of all the angles.
2.(2x)o
(4x-8)o (5x-10)o
pg 111 - 112
![Page 11: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/11.jpg)
TRUE or FALSE?
• If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent.
• Each angle of an equiangular triangle measures 60o.
• In a triangle, there can be at most one right triangle, or at most one obtuse angle.
• The acute angles of a right triangle are complementary.
pg 114
![Page 12: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/12.jpg)
EXTERIOR ANGLES OF A TRIANGLE
• ΔABC has been extended to form exterior angles:
1, 2, & 3.
• Each exterior angle has an adjacent interior angle and two remote interior angles.
• Example:– Exterior angle:– Adjacent interior angle:– Two remote angles:
A
BC
1
23
2
4 5
6
46 & 5
pg 116 - 117
![Page 13: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/13.jpg)
Protractor investigation (exterior and remote interior angles)
• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
• 1 = 4 + 5• 2 = 5 + 6• 3 = 4 + 6
A
BC
1
234 5
6
pg 117
5
4
![Page 14: Triangles 101](https://reader033.vdocuments.site/reader033/viewer/2022052900/5559c89bd8b42a98208b45e7/html5/thumbnails/14.jpg)
Sample Problems: Solve for x.
1.
2.
pg 117
23o
40o
xo
84o
7xo 5xo