Accelerated+Geometry+and+Geometry+and+Informal+Geometry

Geometry Targets:

Students should be able to:

General Geometric Knowledge:

I can accurately name points, lines, planes, angles, rays and segments. I can identify different types of angles including acute, obtuse, right, and straight. I can classify triangles based on the angles and sides.

Parallel Lines:

I can name related angles when parallel lines are cut by a transversal. (Alt. Int. <s, Alt. Ext. <s, Corresponding<s, Same Side Int. <s). I can use the fact that Alt. Int. <s, Alt. Ext. <s, Corresponding<s pairs are congruent both to solve unknown angles and prove lines parallel. I can use the fact that Same Side int <s sum 180 degrees both to solve unknown angles and prove lines parallel.

Congruent Triangles:

- prove two triangles congruent by using SAS, SSS, ASA, HL, AAS congruence theorems. - use the concept of corresponding parts of congruent triangles are congruent - apply the concepts of congruent triangles to solve algebraic problems - use the Isosceles triangle theorem and its converse to solve problems both algebraically and theoretically (proofs)

Indirect Proofs: - use proof by contradiction to prove statements.

Types of Reasoning: Deductive Reasoning: - identify the hypothesis and conclusion of a conditional statement - write an if-then statement based on a condtional statement - write the converse, inverse, and contrapositive of a conditional statement - determine the truth value of the if-then, converse, inverse, and contrapositive and provide counter- examples if they are false. Inductive Reasoning: - use patterns to predict future events or parts of the pattern - look at 2 statements and be able to make a conclusion based on them or determine if there is no conclusion.

Triangles: - I can find points of concurrency such as centroid, incenter, orthocenter and circumcenter. - I can define median, altitude and midsegment and find the lengths of each. - I can prove theorems about the interior and exterior angle measures of triangles. - I can prove the base angles of a triangle are congruent. -

Polygons: - I can define, explain and find the measures of interior and exterior angles.

Quadrilaterals: - name and identify the characteristics of the different types of quadrilaterals (parallelogram, rectangle, square, rhombus, trapezoid, iso. trapezoid, and kite). - draw each type of quadrilateral correctly - know and apply the different ways to prove a quadrilateral is a parallelogram - solve equations using the properties of parallelograms. - know the definition of a median of a trapezoid and know how to find it in a trapezoid.

Triangle Inequalities: - be able to identify the longest to shortest sides of a triangle based on the angle measures - be able to identify the the largest to smallest angles based on the side measurements - use the SAS and SSS inequality theorems to identify relationships between angles and sides in a triangle.

Similar Triangles: -I am able to find the missing sides in a set of similar triangles, given the lengths of at least three sides, in which two are corresponding.

Similar Figures:

Ratios and Proportions:

Right Triangles:

I can identify the hypotenuse. I can find missing angle measures using the Triangle Angle Sum Theorem. I can determine whether or not a triangle is right, obtuse or acute using the Pythagorean Inequalities. I can determine missing lengths in a right triangle using the Pythagorean Theorem. I can define the basic trig ratios in right triangles: sine, cosine and tangent. I can find missing angle measure and side lengths in a right triangle using sine, cosine, and tangent. I can apply the facts of right triangles to real-life situations in a way that helps me to determine missing measurements. I can use scale drawings and trig to solve problems that include unknown distances and angle measures.

Circles: Find arc lengths and areas of sectors of circles. Determine the measures of central and inscribed angles and their associated major and minor arcs. I can find the lengths of chords, radii and diameters within the same circle.

Constructions:

Area:

I can identify the base and height of a rectangle. I can use the base and height correctly to find the area of a rectangle using. I can identify the base and width of a triangle. I can use the base and width correctly to find the area of a triangle using. I can identify the bases and height of a trapezoid. I can use the bases and height correctly to find the area of a trapezoid using. I can identify the apothem, radius, and perimeter of a regular polygon. I can use right triangle trigonometry, and special right triangles to find missing radii, apothems and perimeter. I can use the apothem, radius, and perimeter correctly to find the area of a regular polygon using.

Surface Area and Volume:

Use the ratio of lengths in similar 2-D or 3-D abjects to find the ratio of their areas or volumes. Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base.

Coordinate Geometry:

I can analyze 2-D figures in a coordinate plane using slope and distance to classify a polygon.

Transformations:

I can graph a translation, rotation, dilation and reflection with and without formulas. I can graph compound transformations. I can determine coordinate results of transformations using formulas or by graphing. I can represent transformations within a coordinate system using vectors and matrices. I can identify the reflection and rotation symmetries of 2-D and 3-D figures. I can develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.