Exterior Angles
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Transcript of Exterior Angles
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EXTERIOR ANGLES
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When the sides of a polygon are extended, other angles are formed.
The original angles are the interior angles.
The angles that form linear pairs with the interior angles are the exterior angles.
Angles
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EXTERIOR ANGLE THEOREMAn exterior angle of a triangle…… is equal in measure to the sum of the measures of its two remote interior angles.
remote interior angles Exterior
angle
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EXTERIOR ANGLE THEOREM(YOUR NEW BEST FRIEND)
The measure of an exterior angle in a triangle is the sum of the measures of the 2 remote interior angles
3
2
1 4
exterior angle
remote interioranglesm<1 + m<2 = m<4
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m 1 = m A + ∠ ∠m B ∠
EXTERIOR ANGLE THEOREM
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EXAMPLES
m<G = 60 + 69m<FHG = 180 – 111 = 69 linear pair
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EXAMPLES
x
82°
30° y
Find x & y
x = 68°y = 112°
y = 30 + 82y = 112˚
180 = 30 + 82 + x180 = 112 + x68˚ = x
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EXAMPLESFind m JKM
2x – 5 = x + 70 x – 5 = 70 x = 75
m< JKM = 2(75) - 5m< JKM = 150 - 5m< JKM = 145˚
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EXAMPLESSolve for y in the diagram.
Solve on your own before viewing the
Solution
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4y + 35 = 56 + y3y + 35 = 563y = 21
y= 27
SOLUTION
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EXAMPLESFind the measure of in the diagram shown.1
Solve on your own before viewing the
Solution
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40 + 3x = 5x - 1040 = 2x - 1050 = 2x 25 = x
m < 1= 5x - 10m < 1= 5(25) - 10m < 1= 125 - 10m < 1= 115
SOLUTION
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CHECKPOINT: COMPLETE THE EXERCISES.
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SOLUTION
Right Scalene triangle
x + 70 = 3x + 10
70 = 2x + 1060 = 2x30 = x
3 (30) + 10 = 100˚
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TRIANGLE INEQUALITIES
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Make A Triangle
Construct triangle DEF.
D FF E
D E
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D FF E
D E
Make A Triangle
Construct triangle DEF.
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D E
Make A Triangle
Construct triangle DEF.
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D E
Make A Triangle
Construct triangle DEF.
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D E
Make A Triangle
Construct triangle DEF.
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D E5 3
13
Q:What’s the problem with this?
A: The shorter segments can’t reach each other to complete the triangle. They don’t add up.
Make A Triangle
Construct triangle DEF.
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The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Triangle Inequality Conjecture
Add the two smallest sides; they MUST be larger than the third side
for the triangle to be formed.
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Make A TriangleCan the following lengths form a triangle?1.4 mm
5 mm10 mm
2.2 ft9 ft13 ft
5.10 mm3 mm6 mm
8. 8 m7 m1 m
9.9 mm2 mm1 mm
12.1 mm5 mm3 mm
3.5 cm cm4 cm
√𝟐4. 7 ft
15 ft ft
√𝟏𝟑6. 7 ft
7 ft ft
√𝟕
7.10 mm13 mm mm
√𝟓10.
12 mm22 mm mm
√𝟏𝟑
11.7 mm8 mm mm
√𝟏𝟐
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In a triangle, if one side is longer than another side, then angle opposite the longer side is larger than the other.
Side-Angle Conjecture
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Side-Angle
What’s the biggest side?What’s the biggest angle?What’s the smallest side?What’s the smallest angle?
C
B A
ba
c
bBaA
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Side-Angle
92° 42°
46°
ab
c
Rank the sides from greatest to least.bca
Rank the angles from greatest to least.CAB
A
CB
7
5
4