Geometry proofs &amp; measurement

Coordinate transformations on the plane

I can describe, perform, and compose coordinate transformations and identify how a pre-image maps to an image.

Grade 10 Mathematics

48 lessons

Analyze Chords and Inscribed Angles

Analyze how chords and inscribed angles relate to intercepted arcs and to each other inside the same circle.

Analyze Cross Sections

Analyze the two-dimensional cross-sections formed when planes intersect common three-dimensional solids.

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Analyze Data Distributions

Analyze a data distribution by describing center, spread, shape, and unusual values.

Analyze Polygons in the Coordinate Plane

Analyze a polygon in the coordinate plane by using slope, distance, and structure to classify and describe it.

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Analyze Translations, Rotations, and Reflections

Analyze how translations, rotations, and reflections move figures on the coordinate plane.

Apply Scale Effects to Area and Volume

Apply linear scale factors to determine how area and volume change under dilation.

Apply the Pythagorean Theorem

Apply the Pythagorean theorem to find a missing side length in a right triangle or coordinate model.

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Apply Triangle Congruence Criteria

Apply triangle congruence criteria to decide whether two triangles must be congruent.

Apply Trigonometry to Indirect Measurement

Apply sine, cosine, or tangent to find an unknown height or distance in a right-triangle indirect measurement situation.

Circles and Arcs

Synthesize circle-angle, arc, chord, tangent, and secant ideas to analyze connected circle relationships.

Compare Polynomial, Radical, Rational, and Exponential Behavior

Compare polynomial, radical, rational, and exponential parent functions by using graphs, tables, domain restrictions, and long-run behavior as evidence.

Complete a Grade 10 Capstone Investigation

Complete a multi-step geometry investigation by comparing design options, justifying choices, and communicating a final recommendation.

Complete Segment and Angle Proofs

Complete missing statements and reasons in segment and angle proofs.

Compose Functions

Compose functions by substituting one function into another, evaluating compositions, and explaining how the order of composition affects the result.

Congruence and Rigid Motions

Connect rigid motions to triangle congruence and geometric justification.

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Connect Algebraic and Geometric Representations

Connect a line's coordinates, graph, slope, and equation so each representation supports the others.

Define Sine, Cosine, and Tangent

Define sine, cosine, and tangent as side-length ratios in a right triangle.

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Derive and Apply Area Formulas

Derive familiar area formulas from rearrangements and apply them to triangles, parallelograms, trapezoids, and composite regions.

Develop Deductive Arguments

Build deductive arguments by chaining definitions, given facts, and geometry properties.

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Evaluate Claims Based on Data

Evaluate whether a claim is supported by the data and explain the evidence clearly.

Find and Interpret Inverse Functions

Find the inverse of a one-to-one function, connect the inverse to swapped inputs and outputs, and interpret what inverse notation means in a real situation.

Find Conditional Probabilities

Find conditional probabilities by restricting attention to the given group and interpreting the result in context.

Find Surface Area of Composite Solids

Find the surface area of composite solids by identifying exposed faces, curved surfaces, and hidden shared regions.

Find Volume of Prisms, Pyramids, Cylinders, Cones, and Spheres

Find and compare the volumes of prisms, pyramids, cylinders, cones, and spheres using structure and formula relationships.

Model a Real Situation with Geometry

Turn a real situation into a geometric model, choose a useful figure, and solve for an unknown measurement.

Perform Basic Constructions

Perform and explain basic constructions using a compass and straightedge.

Prove Geometric Relationships with Coordinates

Use slopes, distances, and coordinate reasoning to justify a geometric relationship on the coordinate plane.

Prove Properties of Triangles and Quadrilaterals

Prove key properties of triangles and quadrilaterals by using definitions, angle relationships, and congruent parts.

Prove Theorems Using Similarity

Use triangle similarity to justify a proportional-segments theorem.

Right-Triangle Trigonometry

Connect similarity, special triangles, and trigonometric ratios to solve right-triangle measurement problems.

Similarity and Dilations

Connect dilations, similarity criteria, and proportional side lengths across figures and triangles.

Solve Circle Application Problems

Solve real-world and geometric application problems involving circles by choosing the right measure or formula.

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Solve Proportional Side Length Problems

Solve problems with proportional side lengths in similar figures and triangles.

Solve Right Triangles

Solve a right triangle by using a trigonometric ratio to find a missing side or angle.

Transform Parent Functions

Identify the parent function and describe or write translations, reflections, and vertical stretches or compressions from equations and graphs.

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Understand Arcs and Central Angles

Connect a central angle to its intercepted arc and use that relationship to determine minor arcs, major arcs, and semicircles.

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Understand Dilation

Understand dilation as a transformation that changes size by a scale factor from a center while preserving angle measures and ray direction.

Use Addition and Multiplication Rules

Decide when probability situations use the addition rule and when they use the multiplication rule, then compute the probability accurately.

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Use Counting Principles

Count outcomes and arrangements by multiplying the number of choices at each stage and adjusting factors when choices cannot repeat.

Use Distance and Midpoint Formulas

Use the distance formula and midpoint formula to analyze a segment on the coordinate plane.

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Use Precise Geometric Definitions

Use precise geometric definitions to classify and describe figures and relationships.

Use Special Right Triangles

Use 45-45-90 and 30-60-90 side relationships to find missing side lengths quickly.

Use Tangent and Secant Relationships

Use tangent and secant segment relationships to solve missing lengths in circle diagrams.

Use Transformations to Prove Congruence

Use translations, rotations, and reflections to justify that figures are congruent.

Use Triangle Similarity Criteria

Use triangle similarity criteria to decide whether two triangles must be similar.

Write and Interpret Equations of Circles

Write and interpret equations of circles in standard form and connect each term to the center and radius.

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Write Conditional Statements

Write clear conditional statements from geometric definitions, diagrams, and facts.

Write Equations of Parallel and Perpendicular Lines

Write equations of lines parallel or perpendicular to a given line through a given point.