Circle Proofs Answers 1. Statement Reasons 1. CBE 1. Angles ...
Circle Proofs Answers 1. Statement Reasons 1. CBE 1. Angles ...
Circle Proofs Answers 1. Statement Reasons 1. CBE 1. Angles ...
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<strong>Circle</strong> <strong>Proofs</strong> <strong>Answers</strong><strong>1.</strong><strong>Statement</strong><strong>Reasons</strong><strong>1.</strong> <strong>CBE</strong> ≅ CDE<strong>1.</strong> <strong>Angles</strong> inscribed in the same arc are congruent.2. ABE ≅ ADC2. Supplements of congruent angles are congruent.2.<strong>Statement</strong><strong>Reasons</strong>AB is a diameter<strong>1.</strong> BD is tangent to circle O<strong>1.</strong> Given2. ACB is a right angle 2. An angle inscribed in a semi-circle is a right angle.3. ABD is a right angle 3. A tangent is ⊥ to the diameter at the point of tangency.4. ACB ≅ ABD4. All right angles are congruent.3.<strong>Statement</strong><strong>Reasons</strong><strong>1.</strong> OS ⊥ RT<strong>1.</strong> Given2. REOand TEO areright angles2. ⊥ lines form right angles.3. REOand TEO areright triangles3. A triangle containing a right angle is a right triangle.4. OE ≅ OE4. Reflexive Property≅ 5. All radii in the same circle are congruent.5. RO OT6. REO ≅ TEO7. ROE ≅ EOT8. RS ST 6. Hy - Leg 7. Corresponding parts of congruent triangles are congruent.≅ 8. Congruent central angles have congruent arcs.4.<strong>Statement</strong><strong>Reasons</strong><strong>1.</strong> BD bisects ABC <strong>1.</strong> Given2. DBC ≅ ABD 2. A bisector divides an angle into two congruent angles.3. AD ≅ DC 3. Congruent inscribed angles have congruent arcs.4. AD≅ DC4. Congruent arcs have congruent chords.5. ADC is isosceles 5. If at least two sides of a triangle are ≅ then it is isosceles.5.<strong>Statement</strong><strong>Reasons</strong><strong>1.</strong> B ≅ D<strong>1.</strong> Given2. AD BC2. Given3. C ≅ A4. BC AD5. BC AD6. BCF ≅ ADE7. AE CF 3. If two lines are parallel, alternate interior angles are ≅ .≅ 4. Given≅ 5. ≅ arcs have ≅ chords. 6. ASA ≅ ASA≅ 7. Corresponding parts of congruent triangles are congruent.
6.<strong>Statement</strong><strong>Reasons</strong>AB ⊥ BC<strong>1.</strong>DC ⊥ BC<strong>1.</strong> Given2. Band C are right s 2. ⊥ lines form right angles.3. B ≅ C3. All right angles are ≅ .4. AB ≅ CD 4. Given5. AB ≅ CD5. ≅ arcs have ≅ chords.6. E is the midpoint of BC 6. Given≅ 7. A midpoint divides a line segment into 2 ≅ parts.7. BE EC8. ABE ≅ CED9. AE DE 8. SAS ≅ SAS≅ 9. Corresponding parts of congruent triangles are congruent.7.<strong>Statement</strong><strong>Reasons</strong>BE ⊥ OA<strong>1.</strong>BD⊥OC<strong>1.</strong> Given2. BEOand BDO are2. ⊥ lines form right angles.right angles3. BEOand BDO are3. A triangle with a right angle is a right triangle.right triangles4. BE ≅ BD4. Given≅ 5. Reflexive Property5. BO BO6. BEO ≅ BDO7. BOE ≅ BOC8. AB BC 6. Hy - Leg 7. Corresponding parts of congruent triangles are congruent.≅ 8. ≅ central angles have ≅ arcs.8.<strong>Statement</strong><strong>Reasons</strong><strong>1.</strong> BD bisects ABC <strong>1.</strong> Given2. ABD ≅ CBD2. A bisector divides an angle into two congruent angles.BA⊥AD3.BC ⊥ CD3. Given4. Aand C are right s 4. ⊥ lines form right angles.5. A≅ C5. All right angles are ≅ .6. ADB ∼ CDB6. AA≅AA7. BDA ≅ BDC7. Corresponding angles in similar triangles are congruent.8. AB ≅ BC 8. ≅ inscribed angles have ≅ arcs.9.<strong>Statement</strong><strong>Reasons</strong><strong>1.</strong> Trapezoid ABCD <strong>1.</strong> Given2. AB CD2. In a trapezoid, bases are parallel.3. BC ≅ AD3. Parallel lines intercept congruent arcs.4. BC ≅ AD4. ≅ arcs have ≅ chords.5. Trapezoid ABCD isisosceles5. If the non parallel sides of a trapezoid are ≅ , then the trapezoidis isosceles.A diagram was notgiven in question #9.Other appropriatediagrams are alsoacceptable.
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