Lesson 10.2: Help for Exercises 56-62 on page 610
For Exercises 56 and 57, use the following key ideas, along with congruent triangles, to write a plan. All radii of a circle are congruent (p. 595). The measure of a minor arc is defined to be the measure of its central angle (p. 603). Two arcs of the same circle or of congruent circles are congruent arcs if they have the same measure (p. 604).
For Exercise 58, use the definition of congruent circles (p. 595).
For Exercise 59, follow the plan for proof given. Consider using the HL Congruence Theorem (p. 238) and the definition of the measure of a minor arc (p. 603) as reasons in your proof.
For Exercise 60, notice that the diagram given shows the assumption that center L is not on . A possible contradiction to reach in your indirect proof is that and , while L is not on . You can review the Perpendicular Postulate on page 130.
For Exercises 61 and 62, draw ,
, and . Use the triangles formed.