If you put the three angles of a triangle together they make…
A straight line
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Another proof
Fold point C to AB. The fold should be parallel to AB.
Find x
62
54x
€
x=64°
Find x
x
4x
x
€
4x+ x+ x=180
Find x
x
4x
x
€
6x=180
Find x
x
4x
x
€
x=30°
Can you read French?
Yes, we wanted all angles.
Isosceles triangle
Two sides are the same i.e. AC = BC
Two angles are the same
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∠CAB=∠CBA
Name the base angles
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∠BAB1 and∠BB1A
Find x
x
€
36°
Find x
x
€
36°
= 72
Reason:
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Base∠' s isosΔ
Here’s a hard one. Find the value of . if AB + BP = AQ +QB?
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β
• 1. Extend line AB to a point called R.• 2. Make BR equal in length to BP.• 3. Since AB+BP = AQ+QB, you can prove that AR=AC.• 4. Triangle BRP is an isosceles triangle with the big angle equal to 180
degrees —2 beta.• 5. Thus, angle BRP has to equal beta.• 6. If angle BRP=beta, then angle ACB also equals beta because line AP
bisects angle A.• 7. Therefore the two halves of the chevron formed by points A, R, P, and C
are identical.• 8. If angle C = beta and angle B=2 beta, then beta has to equal 40
degrees for the triangle ABC to add to 180 degrees.
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β is called beta
Angles in a quadrilateral
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180°
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180°
€
360°
Find the angles in the quadrilateral
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360°
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3x
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2x
€
x
€
4x
€
4x+ 3x+ 2x+ x=360
Find the angles in the quadrilateral
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360°
€
3x
€
2x
€
x
€
4x
€
10x=360
€
x=36
Find the angles in the quadrilateral
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360°
€
108°
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72°
€
36°
€
144°
€
10x=360
€
x=36
Find x
Exterior angles
Exterior angles
Exterior angle
Exterior angle equals the sum of the opposite interior angles.