Geometry 3

Level 1

If you put the three angles of a triangle together they make…

A straight line

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are needed to see this picture.

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?

€

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°

€

180°

€

360°

Find the angles in the quadrilateral

€

360°

€

3x

€

2x

€

x

€

4x

€

4x+ 3x+ 2x+ x=360

Find the angles in the quadrilateral

€

360°

€

3x

€

2x

€

x

€

4x

€

10x=360

€

x=36

Find the angles in the quadrilateral

€

360°

€

108°

€

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.

Find the value of x.

70 50

x

Find the value of x.

70 50

x = 70 + 50 = 120