Evidence of Student Vocabulary Knowledge Skills Instructional Achievement Level Descriptors Attainment/Assessment Students: Central angles Students know: Students understand/are able EEG-C.1-3. N/A Given circles with two points to: on the circle, Inscribed angles Definitions and characteristics of central, inscribed, and Explain and justify possible Compare the measures of the Circumscribed angles circumscribed angles in a circle, relationships among central, angles (with and without inscribed, and circumscribed technology) formed by Techniques to find measures of angles sharing intersection creating radii to the given points on the circle, angles including using technology points, creating chords from (dynamic geometry software). a third point on the circle to Accurately find measures of the given points, and creating angles (including using tangents from a third point technology (dynamic outside the circle to the given geometry software)) formed points, and conjecture about from inscribed angles, radii, possible relationships among chords, central angles, the angles, circumscribed angles, and tangents Use logical reasoning to justify (or deny) the Relationships that exist conjectures (in particular among inscribed angles, justify that an inscribed radii, and chords may be angle is one half the central used to find the measures of angle cutting off the same other angles when arc, and the circumscribed appropriate conditions are angle cutting off that arc is given, supplementary to the central angle relating all three). Identifying and justifying relationships exist in geometric figures. Given circles with chords from a point on the circle to the endpoints of a diameter, Find the measure of the
Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Instructional Achievement Level Descriptors Students: Given circles with two points on the circle, Compare the measures of the angles (with and without technology) formed by creating radii to the given points, creating chords from a third point on the circle to the given points, and creating tangents from a third point outside the circle to the given points, and conjecture about possible relationships among the angles, Use logical reasoning to justify (or deny) the conjectures (in particular justify that an inscribed angle is one half the central angle cutting off the same arc, and the circumscribed angle cutting off that arc is supplementary to the central angle relating all three). Given circles with chords from a point on the circle to the endpoints of a diameter, Find the measure of the Central angles Inscribed angles Circumscribed angles Students know: Definitions and characteristics of central, inscribed, and circumscribed angles in a circle, Techniques to find measures of angles including using technology (dynamic geometry software). Students understand/are able to: Explain and justify possible relationships among central, inscribed, and circumscribed angles sharing intersection points on the circle, Accurately find measures of angles (including using technology (dynamic geometry software)) formed from inscribed angles, radii, chords, central angles, circumscribed angles, and tangents Relationships that exist among inscribed angles, radii, and chords may be used to find the measures of other angles when appropriate conditions are given, Identifying and justifying relationships exist in geometric figures. EEG-C.1-3. N/A
Geometry-Pacing-Guide-Version-3.docx