# Geometry [Competency Based] (1st semester)

## Geometry [Competency Based] (1st semester)

## Course Description

What are the different ways a figure can be transformed? What is the difference between similarity and congruence? In Geometry, students formulate mathematical arguments and create geometric constructions. Working with triangle construction to prove theorems, students employ their reasoning abilities to show similarity and congruence, and use trigonometric ratios to find missing measures in triangles. Solving problems concerning three-dimensional figures gives students the opportunity to examine formulas. Students apply their knowledge of geometric shapes by using measures and properties to describe real-life objects, and connect algebra to geometry by graphing figures on the coordinate plane. Students then move to circles, exploring their properties and theorems. Next is the study of probability, in which students interpret data by using independence and conditional probability, and apply the rules of probability to determine compound events and evaluate outcomes of decisions.

## Course Breakdown

- Points, lines, and planes
- Classifying angles and polygons
- Discovering pi
- Mathematical modeling
- Laws of detachment and syllogism
- Planning and writing proofs
- Adjacent, complementary, and supplementary angles
- Slope and intercept of a line
- Parallel lines cut by a transversal
- Congruent segments
- Parallel and perpendicular line construction
- Inscribed shapes inside triangles and circles
- SSS, SAS, and ASA postulates
- Triangle congruency
- Ratios and proportions
- AA, SSS, and SAS similarity tests

## Course Goals

- Apply geometric properties and relationships through inductive and deductive reasoning.
- Explain the building blocks of geometry including using definitions and coordinate geometry.
- Apply the properties of parallel and perpendicular lines.
- Perform geometric constructions.
- Solve problems using the properties of triangles.
- Prove geometric properties and relationships about parallelograms and quadrilaterals by solving problems and using deductive reasoning.
- Prove geometric properties about congruent triangles by solving problems and using deductive reasoning.
- Identify and use the properties of similar polygons and triangles.