* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lesson 10.05H MAIN IDEA (page #) DEFINITION OR SUMMARY
Technical drawing wikipedia , lookup
Euler angles wikipedia , lookup
Integer triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Noether's theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Riemann–Roch theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Area of a circle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Lesson 10.05H MAIN IDEA (page #) DEFINITION OR SUMMARY ____________ The measure of an arc formed by two ____________ arcs is the sum of the measures of the two arcs. EXAMPLE or DRAWING (P1) mPQ + m____________ = mPQR Congruent Arcs Theorem (P1) In the same circle or in two congruent circles, two arcs are congruent if and only if their ____________________. In circle C, WZ ZY and WX Inscribed Angle Theorem (P1) The measure of an ____________ is ____________ the measure of its ____________. m∠DEF = m____________ YZ Lesson 10.05H Congruent Inscribed Angles Theorem (P1) If ____________ of a circle or congruent circles intercept ____________ or the same arc, then the angles are ____________. ∠PQS and ∠PRS intercept PS. ∠PQS ∠____________ Inscribed Angle to a Semicircle Theorem (P1) If an inscribed angle intercepts a ____________, then the angle is a right angle. m∠ABD = ____________ Inscribed Quadrilateral Theorem If a quadrilateral is ____________ in a circle, then its opposite angles are ____________. (P1) m∠Q + m____________ = 180° m____________ + m____________ = 180° Lesson 10.05H STEP 1 You are given an image and the fact that segment AB is congruent to segment ____________. First, set up the two-column table by filling in the given information. STEP 2 Remember, all radii of the same circle are equal in length. Therefore, segments CA, ____________, CX, and ____________ are all congruent. Congruent Arcs and Chords Theorem (P2) STEP 3 Next, by the SSS postulate, triangles ____________ and ____________ are congruent. STEP 4 Knowing that triangle ____________ is congruent to triangle ____________, you can state angle ACB is congruent to angle XCY by ____________, which states that corresponding parts of congruent triangles are congruent. STEP 5 The last step would state that arc ____________ is congruent to arc ____________ because of the Congruent Arcs Theorem, which states that two arcs are congruent if the central angles that intercept them are also congruent. Applying the Perpendicular Diameters and Chords Theorem (P3) Segments AM and MB are equal in length as are the lengths of arcs EA and EB. Therefore, CE bisects AB at point M. AB also bisects arc AB at point E. This illustrates the Perpendicular Diameters and Chords Theorem, which states that if a diameter is ____________ to a chord, then the diameter ____________ the chord and the minor arc between the endpoints of the chord. Given: Circle C with congruent chords AB and XY. Prove: AB XY Lesson 10.05H