Download Geometry Standards with Learning Targets

GEOMETRY - SEMESTER 2 STANDARDS AND LEARNING TARGETS
STANDARD 9A: Right Triangles (Pythagorean Theorem/Converse and Special Right Triangles)
(CCSS: G.SRT.4, G.SRT.8; 8-10 days)
Students will be able to:
a) Express square roots in equivalent radical form and their decimal approximations when appropriate.
b) Find the unknown side length of a right triangle using Pythagorean Theorem
c) Determine if three lengths form a triangle.
d) Classify a triangle as acute, right or obtuse based on its side lengths.
e) Find the unknown side lengths of a 45-45-90 triangle.
f) Find the unknown sides lengths of a 30-60-90 triangle.
STANDARD 9B: Right Triangles (Basic Trigonometry)
(CCSS: G.SRT.6, G.SRT.7, G.SRT.8, G.MG.1; 8-10 days)
Students will be able to:
a) Understand by similarity the trigonometric ratios (sine, cosine, tangent) and be able to find the
unknown side lengths of a right triangle using trigonometric ratios.
b) Find the measure of an unknown acute angle of a right triangle using trigonometric ratios.
c) Apply trigonometry to calculate unknown heights/lengths in a variety of figures (ie parallelograms,
trapezoids, etc.)
d) Apply trigonometry to solve a variety problems.
STANDARD 10: Apply Trigonometry to General Triangles
(CCSS: G.SRT.9, G.SRT.10, G.SRT.11; 6-8 days)
Students will be able to:
a) Derive the formula A = (1/2)absin C and be able to apply the formula to compute the area of a triangle.
b) Understand the derivation of the Law of Sines and be able to apply the Law of Sines to find unknown
measurements in right and non-right triangles.
c) Understand the derivation of the Law of Cosines and be able to apply the Law of Cosines to find
unknown measurements in right and non-right triangles.
STANDARD 11: Regular Polygons – Sides, Angles and Area
(CCSS: G.MG.1, G.MG.3; 8-10 days)
Students will be able to:
a) Find the measure of an interior angle, exterior angle, or sum of the interior angles given a regular
polygon.
b) Determine the number of sides of a regular polygon given an interior angle, exterior angle or sum of its
interior angles.
c) Given one of the following dimensions of a regular polygon, determine the other dimensions:
perimeter, side length, radius, apothem
d) Find the perimeter and area of a regular polygon, including composite shapes and shaded regions.
STANDARD 12: Circles - Arc Length and Areas
(CCSS: G.C.3, G.C.5; 8-10 days)
Students will be able to:
a) Identify minor arcs, major arcs and semicircles and find their measures given the measure of a central
angle and/or other arc measures.
b) Find the length of an arc (arc length).
c) Find the area of a sector of a circle.
d) Find the area of shaded regions in circles (including rings and segments) and shapes involving circles.
e) Construct the inscribed and circumscribed circles of a triangle.
f) Find the area of an inscribed and area of a circumscribed circle for a regular polygon.
g) Compute area probabilities involving shaded regions/areas involving circles.
STANDARD 13: Circles - Arcs and Angle Relationships
(CCSS: G.C.2, G.C.3; 8-10 days)
Students will be able to:
a) Identify and apply relationships between a tangent(s) to a circle.
b) Identify, describe and apply relationships among central angles, inscribed angles, radii, and chords.
c) Find measures of angles and arcs formed by the intersection of chords, secants, and tangents.
d) Construct the inscribed and circumscribed circles of a triangle. (May be taught in earlier unit.)
STANDARD 14: Circles in the Coordinate Plane – Equations and Graphs of Circles
(CCSS: G.C.1, G.GPE.1, G.GPE.4; 8-10 days)
Students will be able to:
a) Derive the equation of a circle of given center and radius using the Pythagorean Theorem
b) Find the center and radius of a circle given its equation in standard form.
c) Graph a circle given it's equation in standard form.
d) Determine if a point lies inside, on, or outside the circle given its equation.
e) Find the equation of a circle in standard form given information related to the circle (ie center and point
on circle, center and equation of line tangent to circle, endpoints of diameter of circle, etc.).
f) Complete the square to find the center and radius of a circle given by an equation.
g) Prove circles are similar.
STANDARD 15: Volume
(CCSS: G.GMD.3, G.GMD.4; 8-10 days)
Student will be able to:
a) Find the volume of right prisms, including the use of Cavalieri's Principle
b) Find the volume of cylinders, including the use of Cavalieri's Principle
c) Find the volume of regular pyramids.
d) Find the volume of right cones.
e) Find the volume of spheres.
f) Find the volume of composite solids involving right prisms, regular pyramids, cylinders, cones and
spheres.
g) Apply volume formulas to find missing dimensions of solids.
h) Apply volume formulas to solve a variety of problems.