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Geometry 3
Level 1
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
x  64 x
54
Find x
4x
4x  x  x  180
x
x

Find x
4x
6x  180
x
x

Find x
4x
x  30
x
x

Can you read French?
Yes, we wanted all angles.
Isosceles triangle
Two angles are
the same
Two sides are the
same i.e. AC = BC
CAB  CBA

Name the base angles
BAB1 and BB1 A
Find x
36

x
Find x
36
Reason:
Base 's isos 

x
= 72

Here’s a hard one. Find the value of .
if AB + BP = AQ +QB?

 is called beta
•
•
•
•
•
•
•
•
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.
Angles in a quadrilateral
180
360
180



Find the angles in the quadrilateral
4x
x
3x


2x


4x  3x  2x  x  360

360
Find the angles in the quadrilateral
4x
x
360
3x

2x



10x  360

x  36
Find the angles in the quadrilateral
144
36
360
108


72


10x  360
x  36
Find x
Exterior angles
Exterior angles
Exterior angle
Exterior angle equals the sum of the
opposite interior angles.
Find the value of x.
x
70
50
Find the value of x.
x = 70 + 50 = 120
70
50