WHCSD Scope and Sequence	Geometry	2021-2022

Geometry Scope and Sequence

Domain | Quarter 1 44 Days | Quarter 2 41 Days | Quarter 3 41 Days | Quarter 4 47 Days
Content | Content | Content | Content

CONGRUENCE G.CO

SIMILARITY, RIGHT TRIANGLES, AND TRIGONOMETRY G.SRT

CIRCLES G.C.

EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS	G.GPE

GEOMETRIC MEASUREMENT AND DIMENSION
G.GMD

CONDITIONAL PROBABILITY AND THE RULES OF PROBABILITY S.CP.

G.CO.1 Know precise definitions of ray, angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and arc length.
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not, e.g., translation versus horizontal stretch. G.CO.3 Identify the symmetries of a figure, which are the rotations and reflections that carry it onto itself. a. Identify figures that have line symmetry; draw and use lines of symmetry to analyze properties of shapes. b. Identify figures that have rotational symmetry; determine the angle of rotation, and use rotational

G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations G to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.4 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: a line parallel to one side of a triangle

G.C.1 Prove that all circles are similar using transformational arguments. G.C.2 Identify and describe relationships among angles, radii, chords, tangents, and arcs and use them to solve problems. Include the relationship between central, inscribed, and circumscribed angles and their intercepted arcs; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G.C.3 Construct the inscribed and circumscribed circles of a triangle; prove and apply the property that opposite angles are supplementary for a quadrilateral inscribed in a circle. (+)
G.C.4 Construct a tangent line from a point outside a given circle to the circle.

G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. (+) G.GPE.2 Derive the equation of a parabola given a focus and directrix. (+)
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically and to verify geometric relationships algebraically, including properties of special triangles, quadrilaterals, and circles. For example, determine if a figure defined by four given points in the coordinate plane is a rectangle; determine if a specific point lies on a given circle. (G, M2)
G.GPE.5 Justify the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems, e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point.
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. G.GPE.7 Use coordinates to compute perimeters

Note: The following standards are |
not currently aligned to any of the 4
marking periods: |

WHCSD Scope and Sequence	Geometry	2021-2022

symmetry to analyze properties of shapes.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using items such as graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Understand congruence in terms of rigid motions. G.CO.6 Use geometric descriptions of rigid motionsG to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the

divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.
Define trigonometric ratios, and solve problems involving right triangles.
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.8 Solve problems involving right triangles. a. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems if one of the two acute angles and a side length is given. (G, M2) (+) b. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. (A2, M3)
Apply trigonometry to general triangles. (+)
G.SRT.9 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary

Find arc lengths and areas of sectors of circles.
G.C.5 Find arc lengths and areas of sectors of circles. a. Apply similarity to relate the length of an arc intercepted by a central angle to the radius. Use the relationship to solve problems. b. Derive the formula for the area of a sector, and use it to
solve problems.
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. G.GMD.4 Identify the shapes of two-dimensional cross-sections of
three-dimensional objects, and identify
three-dimensional objects generated by rotations of two-dimensional objects.

of polygons and areas of triangles and rectangles, e.g., using the distance formula.

S.CP.1 Describe events as subsets of |
a sample space (the set of |
outcomes) using characteristics (o categories) of the outcomes, or as | r
unions, intersections, or |
complements of other events (“or,” |
“and,” “not”).★ |
S.CP.2 Understand that two events A |
and B are independent if and only i the probability of A and B occurring | f
together is the product of their |
probabilities, and use this |
characterization to determine i | f
they are independent.★ |
S.CP.3 Understand the conditional probability of A given B as P(A and |
B)/P(B), and interpret independence |
of A and B as saying that the |
conditional probability of A given B |
is the same as the probability of A | ,
and the conditional probability of B |
given A is the same as the |
probability of B.★ |
S.CP.4 Construct and interpret |
two-way frequency tables of data |
when two categories are associate | d
with each object being classified. |

WHCSD Scope and Sequence	Geometry	2021-2022

definition of congruence in terms of rigid motions.

Prove geometric theorems both formally and informally using a variety of methods. G.CO.9 Prove and apply theorems about lines and angles. Theorems include but are not restricted to the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. G.CO.10 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. G.CO.11 Prove and apply theorems about parallelograms. Theorems include but are not restricted to the following: opposite sides are congruent, opposite angles are congruent, the

line from a vertex perpendicular to the opposite side. (+) G.GMD.5 Understand how and when changes to the measures of a figure (lengths or angles) result in similar and non-similar figures. G.GMD.6 When figures are similar, understand and apply the fact that when a figure is scaled by a factor of k, the effect on lengths, areas, and volumes is that they are multiplied by k, k2, and k3, respectively.

Use the two way table as a sample

space to decide if events are |
independent and to approximate |
conditional probabilities. For example, collect data from a |
random sample of students in your |
school on their favorite subject |
among math, science, and English | .
Estimate the probability that a |
randomly selected student from |
your school will favor science given |
that the student is in tenth grade | .
Do the same for other subjects and |
compare the results.★ |
S.CP.5 Recognize and explain the |
concepts of conditional probabilit | y
and independence in everyda | y
language and everyday situations. |
For example, compare the chance o | f
having lung cancer if you are a |
smoker with the chance of being a |
smoker if you have lung cancer.★ |
S.CP.6 Find the conditional |
probability of A given B as the |
fraction of B’s outcomes that also |
belong to A, and interpret the |
answer in terms of the model.★ |
S.CP.7 Apply the Addition Rule, P( | A
or B) = P(A) + P(B) − P(A and B), an | d
interpret the answer in terms of the |
model.★(+) |
Apply the general Multiplication |
Rule in a uniform probability |
modelG, P(A and B) = P(A)⋅P(B|A) | =
P(B)⋅P(A|B), and interpret the |
answer in terms of the model.★(G, |
M2) (+) |
Use permutations and combinations |
to compute probabilities o | f

WHCSD Scope and Sequence	Geometry	2021-2022

diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle
G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove and apply theorems both formally and informally involving similarity using a variety of methods.

compound events and solve

problems.★(G, M2) |

Resources

CPM (College Preparatory Math)
ODE Model Curriculum GAISE model framework

CPM (College Preparatory Math) ODE Model Curriculum
GAISE model framework Kahn Academy

CPM (College Preparatory Math)
ODE Model Curriculum GAISE model framework

CPM (College Preparatory Math) ODE Model Curriculum
GAISE model framework Kahn Academy

WHCSD Scope and Sequence	Geometry	2021-2022

| Kahn Academy | | Kahn Academy |

Notes:

Mathematical Practices
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.
5. Use appropriate tools strategically. 6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.