## Geometry

 Course code: GMT0237 School: Generic Created by: Theodore Droseros Subject: Geometry Modified on: 22-Jun-2013 Grades: 9

### Description:

This course examines two and three dimensional geometric figures and their properties. Emphasis is placed on the use of inductive and deductive reasoning to solve problems. Points, segments, triangles, polygons, circles, and solid figures are the structures studied. The focus of this course is on the comparisons of these structures and how they relate to surface area, volume, congruency, similarity, and transformations. Knowledge of Algebra I is needed for this course.

Units in this course (12)
18 Items

Intro to Geometry

This Unit focuses on the building blocks of geometry. The major themes include describing and measuring geometric figures, and understanding the properties of equality and congruence.

• Subject: Geometry

Tags: points,lines,planes,segments,congreuence,midpoint,classify angles,classify polygons,angle pair,angle pair relationships,distance formula

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12 Items

Reasoning and Proof

This Unit explores the elements of reasoning and how to use it to prove theorems about angle pairs and segments. It also introduces the properties of congruence, which will also be used in proofs. The major themes in these Unit include inductive and deductive reasoning, and understanding and writing proofs of geometric relationships.

• Subject: Geometry

Tags: inductive reasoning,deductive reasoning,conditional statements,postulates,converse,inverse,angle pair,statements,segments,patterns,logic,two-column proof,theorems,if-then,counterexample

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Parallel and Perpendicular Lines

The Unit discusses the different relationships formed by parallel and perpendicular lines. It demonstrates how proofs and theorems are used to prove lines are parallel or perpendicular. There is also a review of equations of lines of slopes and review questions at the end of each section.

• Subject: Geometry

Tags: line pairs,angle pairs,parallel,perpendicular,transversals,graph,line,slope,equations,proofs,theorems,angle measures,slope-intercept,interior angles,exterior angles,corresponding angles,skew lines

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18 Items

Congruent Triangles

This Unit introduces the different properties of triangles. It focuses on classifying triangles by sides and angles and using a number of theorems to prove that two triangles are congruent.

• Subject: Geometry

Tags: triangle,scalene,equilateral,isosceles,corresponding,interior angles,exterior angles,equiangular,proof,theorem,congruent figures,right triangle,corollary

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Relationships within Triangles

This Unit further examines methods for justifying and proving relationships within triangles. The main ideas include how the properties of special segments can be used to complete proofs and how to use inequalities to make comparisons among triangles.

• Subject: Geometry

Tags: midsegment,midsegment theorem,perpendicular bisectors,angle bisector,medians,altitudes,inequalities,indirect proof,coordinate proof,concurrency,equidistant,geometry,triangles,theorems,segments

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20 Items

This Unit concentrates on the properties of various types of polygons. The major themes include using angle relationships in polygons, using properties of parallelograms, and classifying different types of quadrilaterals by their properties.

• Subject: Geometry

Tags: diagonal,geometry,midsegment of a trapezoid,rhombus,square,rectangle,kite,trapezoid,parallelogram,base,legs,leg,base angle

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Similarity

This Unit introduces the concept of similarity and how it relates to polygons, quadrilaterals, and triangles. It discusses how to use ratios and proportions to solve geometry problems and eventually extends the the idea of proportionality to parallel lines.

• Subject: Geometry

Tags: ratio,proportions,geometry,scale,scale factor,means,similar polygons,AA,SSS,SAS

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Right Triangle Trigonometry

This Unit examines right triangles in more depth. It explores the Pythagorean Theorem, special relationships in right triangles, and how to use trigonometric ratios to solve right triangles.

• Subject: Geometry

Tags: pythagorean theorem,pythagorean converse,tangent,cosine,sine,adjacent,hypotenuse,inverse cosine,inverse tangent,inverse sine,geometry,geometric mean

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Properties of Circles

This Unit explores all parts of the circle. The major themes include the different segments that intersect circles, applying angle relationships in circles, and finally circles in the coordinate plane.

• Subject: Geometry

Tags: center,radius,diameter,secant,tangent,major arc,arc,standard equation of a circle,minor arc,central angle,congruent circles,chord,geometry

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Perimeter and Area

This Unit focuses on measuring the length and area of the shapes that have already been discussed in previous units. The major topics in this Unit include using area formulas for polygons, relating perimeter and area ratios in similar polygons, and comparing measures for parts of a circle to the entire circle.

• Subject: Geometry

Tags: circumference,radius of a polygon,geometry,probability,arc length,bases of parallelogram,center of a polygon,trapezoids,rhombus,kites,similar polygons

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14 Items

Surface Area and Volume

This Unit examines surface area and volume. The major themes include exploring solids and their properties, solving problems using the properties of surface area and volume, and connecting the concept of similarity to solids.

• Subject: Geometry

Tags: cylinder,prism,sphere,pyramid,cones,face,edge,geometry,similar solids,right prism,right cylinder

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9 Items

Transformations

This Unit explores transformations. The main topics include performing congruence and similarity transformations, using symmetry and tessellations, and applying matrices and vectors in geometry.

• Subject: Geometry