Learning Resources

Focus E: Proving Relationships

Test yourself (solution)

1. Given: DE @ FE and DC @ FC.
Prove: @

Proof:

1. DE @ FE (given)

2. @ (congruent chords intercept congruent arcs)

3. DC @ FC (given)

4. @ (congruent chords intercept congruent arcs)

5. + @ + (adding like terms together)

6. @ (adding arcs)

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2. In the diagram below, m = 56° and m = 54°
Find: a, b, c, d, e, f

a = ½ (m ) (inscribed angle is half the intercepted arc)
= 28°

d = m (central angle is equal to the intercepted arc)
= 54°

e = 180° - d = 180° - 54°
= 126°

b = ½ (e) (inscribed angle half the central angle)
= 63°

c = ½ ( m ) (inscribed angle is half the intercepted arc.)
= 27°

f = 180° - ( a + b + c) (sum of the angles of a triangle = 180°)
= 180° - 118°
= 162°

Note that b + c = 90° as it should be for an angle in a semicircle.