Geometry
Fall Semester | ||||||
Unit Title | Unit 1: Points, Lines, and Planes with Logical Reasoning | Unit 2: Parallel and Perpendicular Lines with Logical Reasoning | Unit 3: Congruent Triangles | Unit 4: Relationships in Triangles | Unit 5: Proportions and Similarity | Unit 6: Right Triangles and Trigonometry |
Time | ~ 4 weeks | ~ 4 weeks | ~ 3 weeks | ~ 3 weeks | ~ 2 weeks | ~ 4 weeks |
Understandings | Geometry is an axiomatic system using defined and undefined terms which work together to form fundamental geometric relationships.
The distance formula is derived from the Pythagorean Theorem.
Constructions are used to investigate and verify geometric relationships. Conjectures are used to make predictions about geometric relationships.
| Common properties among various linear relationships exist and can be validated or proven algebraically, transformationally, and through constructions.
Conjectures can be written using patterns in a sequence.
Angle pairs are formed when parallel lines are cut by transversals.
The special angle pairs formed by parallel lines and a transversal are either congruent or supplementary.
| Constructions validate conjectures about relationships in triangles and support understanding of conditions required to prove triangle congruence.
Perpendicular lines verify triangle congruence by the Hypotenuse-Leg Congruence Theorem.
Two triangles can be proven to be congruent without having to show that all corresponding sides and angles are congruent.
| Constructions of triangle segments generate points of concurrency that serve as centers of the triangle, each important for various purposes.
Properties of points of concurrency can be verified by the construction of special segments with a straightedge and the folding of a triangle.
Constructions can be used to verify conjectures about triangle relationships.
Any point on the perpendicular bisector of a segment can be proven to be equidistant from each of the segment's endpoints. | Special side and angle relationships that are characteristic of similar figures can be used to determine unknown measurements between similar figures and prove their similarity.
Similar triangles can be identified and verified if two angles of one triangle are congruent to two angles of another triangle.
Proportional changes in a figure refers to changing each dimension by a scale factor. Non-proportional changes in a figure refers to changing the dimensions of the figure by different scale factors.
| Right triangles hold special properties that can be used to solve real-world problems.
Trigonometric ratios are used to find missing measures of sides.
Angle measures can be found using inverse trigonometric ratios.
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TEKS | G.2 A, B G.4 A G.5 B, C | G.2 B, C G.4 A, B, C G.5 A, B G.6 A | G.2 B G.5 A, B G.6 B, D | G.5 A, C, D G.6 A, D | G.6 D G.7 A, B G.8 A G.10 B | G.6 D G.8 B G.9 A, B |
Process Standards | G.1 A, B, C, D, E, F, G | |||||
Geometry
Spring Semester | ||||||
Unit Title | Unit 7: Quadrilaterals | Unit 8: Transformations and Symmetry | Unit 9: Circles | Unit 10: Areas of Polygons and Circles | Unit 11: Extending Surface Area and Volume | Unit 12: Probability |
Time | ~ 2 weeks | ~ 2 weeks | ~ 3 weeks | ~ 3 weeks | ~ 2 weeks | ~ 2 weeks |
Understandings | Side and angle relationships exist among special cases of quadrilaterals that can be used to determine unknown measurements and verified by using the distance, midpoint, and/or slope formulas.
Patterns can be used to make conjectures about the sum of the interior and exterior angles of a polygon.
Patterns can be used to make conjectures about the criteria (sides, angles, and diagonals) required for special quadrilaterals.
| Generating, describing, and differentiating between various rigid and non-rigid transformations can be helpful in understanding real-world applications and making connections to higher level mathematics.
The ratio of the perimeter of similar figures is equal to the ratio of the sides of the same similar figures. Proportional changes in a figure refers to changing each dimension by a scale factor.
Two similar polygons have areas that are proportional to the square of the scale factor.
| Connections between algebra and geometry can be made through angle and segment relationships unique to circles.
The distance, slope, and midpoint formulas are used to verify segment and angle relationships in circles.
A quadrilateral is inscribed in a circle if its opposite angles are supplementary.
A polygon is inscribed in a circle if all of its sides are chords in the circle.
A polygon is circumscribed about a circle if all the sides are tangent to the circle.
A central angle has the same degree measure as its intercepted arc. | Area of a geometric object depends on the measures of its two dimensional shape.
Two similar polygons have areas that are proportional to the square of the scale factor.
The area formula for a parallelogram is derived using the area formula for a rectangle.
The area formula for a rhombus can be derived using multiple methods.
| Surface area and volume of a geometric object depends on the measures of its three-dimensional shape.
Area of a composite figure is determined by the sum of the areas of the simple shapes.
Composite area can be used to derive surface area formulas.
vVolume of a composite figure is the sum of the volumes of the combined figures.
| Probability can be understood and used in geometric contexts as well as everyday life.
Theoretical probability is the probability based on reasoning, whereas experimental probability is based on performing an experiment.
Two events are independent when the probability of one event does not affect the probability of the other event from occurring.
Two events are dependent when the probability of one event does affect the probability of the other event from occurring.
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TEKS | G.2 B G.5 A, C G.6 E | G.3 A, B, C, D G.6 C G.7 A G.10 A, B | G.2 B G.5 A G.12 A, B, D, E | G.10 B G.11 A, B G.12 C | G.4 D G.10 A, B G.11 B, C, D | G.13 A, B, C, D, E |
Process Standards | G.1 A, B, C, D, E, F, G | |||||