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Common Core: Math
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 Student Outcomes Students apply the law of sines or the law of cosines to determine missing measurements in realworld situations that can be modeled using nonright triangles, including situations...

 Student Outcomes Students prove the law of cosines and use it to solve problems.

 Student Outcomes Students prove the law of sines and use it to solve problems.

 Student Outcomes Students prove the formula Area = 1/2 bc sin(A) for a triangle. They reason geometrically and numerically to find the areas of various triangles.

 Student Outcomes Students construct a tangent line from a point outside a given circle to the circle.

 Student Outcomes Students will be able to give an informal argument using Cavalieri’s principle for the formula for the volume of a sphere and other solid figures.

 Student Outcomes Students learn to graph equations of the form x2/a2  y2/b2 =1 . Students derive the equations of hyperbolas given the foci, using the fact that the difference of distances from the...

 Student Outcomes Students derive the equations of ellipses given the foci, using the fact that the sum of distances from the foci is constant.

 Student Outcomes Students convert between the real and complex forms of equations for ellipses. Students write equations of ellipses and represent them graphically.

 Student Outcomes Students determine the area of a cyclic quadrilateral as a function of its side lengths and the acute angle formed by its diagonals. Students prove Ptolemy’s theorem, which states...

 Student Outcomes Students show that a quadrilateral is cyclic if and only if its opposite angles are supplementary. Students derive and apply the area of cyclic quadrilateral ABCD as 1/2 AB·CD·sin(w...

 Student Outcomes Given a circle, students find the equations of two lines tangent to the circle with specified slopes. Given a circle and a point outside the circle, students find the equation of the...

 Student Outcomes Students complete the square in order to write the equation of a circle in centerradius form. Students recognize when a quadratic in x and y is the equation for a circle.

 Student Outcomes Students write the equation for a circle in centerradius form, (x  a)2 (y  b)2 = r2 using the Pythagorean theorem or the distance formula. Students write the equation of a circle...

 Student Outcomes Students find “missing lengths” in circlesecant or circlesecanttangent diagrams.

 Student Outcomes Students find the measures of angle/arcs and chords in figures that include two secant lines meeting outside a circle, where the measures must be inferred from other data.

 Student Outcomes Students understand that an angle whose vertex lies in the interior of a circle intersects the circle in two points and that the edges of the angles are contained within two secant...

 Student Outcomes Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays...

 Student Outcomes Students use tangent segments and radii of circles to conjecture and prove geometric statements, especially those that rely on the congruency of tangent segments to a circle from a...

 Student Outcomes Students discover that a line is tangent to a circle at a given point if it is perpendicular to the radius drawn to that point. Students construct tangents to a circle through a...

 Student Outcomes Students apply their understanding of arc length and area of sectors to solve problems of unknown area and length.

 Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a...

 Student Outcomes Congruent chords have congruent arcs, and the converse is true. Arcs between parallel chords are congruent.

 Student Outcomes Define the angle measure of arcs, and understand that arcs of equal angle measure are similar. Restate and understand the inscribed angle theorem in terms of arcs: The measure of an...