Triangles Part 1 The sum of the angles in a triangle is always equal to: 180°
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Transcript of Triangles Part 1 The sum of the angles in a triangle is always equal to: 180°
![Page 1: Triangles Part 1 The sum of the angles in a triangle is always equal to: 180°](https://reader030.fdocuments.us/reader030/viewer/2022032415/56649f045503460f94c18b87/html5/thumbnails/1.jpg)
Triangles Part 1
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The sum of the angles in a triangle is always equal to:
180°
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Classification By Angle
AcuteA triangle that has all 3 acute angles
ObtuseA triangle with one obtuse angle and 2 acute angles
RightA triangle with 1 right angle and 2 acute angles
The two acute angles must = 90° therefore they are complimentary
EquiangularA triangle with all 3 angles congruent
They must each = 60 °
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Classification by Sides
ScaleneAll three sides have different lengths
IsoscelesTwo sides have the same length
Equilateral All three sides have the same length
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Isosceles Triangles
B
A C
AB = CB and <A = < C
Leg Leg
Base
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Equilateral Triangle
An equilateral triangle is also equiangular.
An equiangular triangle is also equilateral
B
A C
AB = BC = AC <A = <B = <C
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Classify each triangle by its angles and sides.
Equilateral
Scalene, Right
Isosceles, Acute
Isosceles, Obtuse
Scalene, Acute
Isosceles, Right
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Using the Distance Formula to classify triangles by their sides
Find the measure of the sides of triangle DCE,
then classify the triangle by sides. D(3,9);E(−5,3);C(2,2)
Step 1: Find the distance of all three sides using the distacneformula. D = (x
2- x1)2 + (y
2- y1)2
DE = (-5 - 3)2 + (3-9)2= (-8)2+(-6)2 = 64+36 = 100 = 10
EC =
DC =
Step 2: Classify the traingle
Since _____ sides are congruent the traingle is called ______
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You Try
Find the measure of the sides of RST. Classify the triangle by sides.
RST is Scalene
R(−1.−3);S(4,4);T(8,−1)
RS = 74;ST = 41;RT = 85
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Find the missing Values
Find x and the measure of each side of an equilateral triangle RST if:
RS =x+ 9;ST =2x;RT =3x−9
2x
3x-9
x+9
Step 1: Draw and equilateraltraingle and label the giveninformation.
S
R T
3x-9 = 2x -9 = -x 9 = x
x+9 = 3x - 9 9 = 2x - 9 18 = 2x 9 = x
x+9 = 2x 9 = x
2x
3x-9
x+9
Step 1: Draw and equilateraltraingle and label the giveninformation.
Step 2: Set any 2 sidesequal to eachother andsolve for x. (It does notmatter which two sides youchoose since all three areequal)
S
R T
RT = 3x-9 RT = 3(9)-9RT = 27-9RT = 18
ST = 2x ST = 2(9)ST = 18
RS = x + 9 RS = 9 + 9 RS = 18
x = 9
2x
3x-9
x+9
Step 1: Draw and equilateral traingleand label the given information.
Step 2: Set any 2 sides equal toeachother and solve for x. (It doesnot matter which two sides youchoose since all three are equal)
Step 3: Plug x into one side to getall three side lengths. (To checkyour answer plug x into the othertwo sides and make sure all threesides are equal.)
S
R T
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You Try
Find d and the measure of each side of an equilateral triangle KLM if:
KL =d+ 2;LM =12 −d;KM =4d−13
d =5;KL =LM =KM =7
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One more! (This one is a little different)
Find x and the measure of all sides if COW is
isosceles, with CO=CW, and CO =x+ 7;CW =3x−5;OW =x−1
x =6;CO=13,CW =13,OW =5
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Finding the Measure of Missing Angles
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The sum of the angles in a triangle is always equal to:
180°
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Examples
Find X:
39°65°
x40°
x
30°
2x
x x
1.)2.)
3.) 4.)
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Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles.
Exterior Angle: An angle formed when one side of a triangle is extended
Remote Interior Angles: The interior angles of the triangle that are not adjacent to the exterior angle
m∠1 + m∠2 = m∠4
∠4 is an exteriorangle
∠1 & ∠2 are remote interior angles to∠4
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Proof of Exterior Angle Theorem
1.) m∠1 + m∠2 + m∠3 = 180 By Def of a Triangle
2.) m∠3 + m∠4 = 180 By Def of Liner Pair
3.) m∠1 + m∠2 + m∠3 = m∠3 + m∠4 By Substitution
4.) m∠1 + m∠2 = m∠4 By SPOE
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Bigger Picture
Find all missing angles
5
4 32
1
38°
32°
41°64°